81 Similarity in Right Triangles


 Darlene Burns
 4 years ago
 Views:
Transcription
1 81 Similarity in Right Triangles In this chapter about right triangles, you will be working with radicals, such as 19 and 2 5. radical is in simplest form when: 1. No perfect square factor other then 1 is under the radical sign. 2. No fraction is under the radical sign. 3. No fraction has a radical denominator. irections: Simplify lasswork: p.288 E # Note: Radicals should always be written in simplest form If a, b, and are positive numbers and a = b then is the geometric mean between a and b. Notice that by multiplying means/etremes 2 = ab and by taking the square root of each side = ab. asically, to find the geometric mean of two # s, multiply them and take the square root. Note: The geometric mean always falls between the two numbers. irections: Find the geometric mean between the two numbers and and and and and 24 Review: altitude, hypotenuse Theorem: If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. Note: ~ ~ has a different measure in all 3 s.
2 The following two corollaries are true because of the similar s. orollary 1: When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse. Y orollary 2: When the altitude is drawn to the hypotenuse of a right triangle, each is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that. X Z Eamples and informal statements of these two corollaries are given. or 1 X Y = Y Z piece of hypotenuse altitude altitude = other piece of hypotenuse or 2 or 2 For XY : For YZ : XZ XY XZ YZ = = XY X YZ Z hypotenuse = piece of hyp. adj. to irections: Eercises refer to the diagram at right. 12. If N = 8 and N = 16, find N. N 13. If N = 4 and N = 12, find N. 14. If N = 4 and N = 8, find. 15. If = 18 and = 12, find N. 16. If = 6 and N = 4, find N.
3 82 The Pythagorean Theorem Radicals: Eample: p.291 #5, 6, 9 You do: p.291 #78, Pythagorean Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the s. Find the value of. Use diagram for #18. If in is a right angle, then Proof on p.290 a + b = c. b a c Reminders:. The diagonals of a rhombus are bisectors of each other.. The altitude drawn to the base of an isosceles triangle is to and bisects the base. Find the value of
4 Find the length of the diagonals of a square with perimeter The diagonals of a rhombus have lengths 18 and 24. Find the perimeter of the rhombus. 19. rectangle has diagonals of 5 cm and its width is 3 cm. Find the length of the rectangle. 20. The perimeter of a rhombus is 100 cm, and one diagonal is 48 cm long. Find the length of the other diagonal.
5 83 The onverse of the Pythagorean Theorem Review: Theorems learned T81 ~ ~ or 1 or 2 Since ~ Since ~ = = The Pythagorean Theorem says: If is a right triangle, then a + b = c. The converse is also true: If a + b = c, then is a right triangle. Theorem: If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. c a b irections: If a triangle is formed with sides having the lengths given, it is a right triangle? 1. 4, 7, , 21, , 2, , 1.5, 1.7 triangle with sides 3, 4, and 5 is a right triangle because = 5. ny triangle with sides 3n, 4n, and 5n, n > 0,is also a right triangle because (3 n) + (4 n) = (5 n). Multiples of any three lengths that form a right triangle will also form right triangles. These groups of three lengths are called Pythagorean triples. If you use them, you can save time and effort. 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 6, 8, 10 10, 24, 26 16, 30, 34 14, 48, 50 9, 12, 15 15, 36, 39 24, 45, 51 21, 72,
6 2 These theorems say that by comparing c and a 2 + b 2, you can determine if a triangle is acute, right, or obtuse. Note: c is always largest side. If c = a + b, then If c > a + b, then If c < a + b, then is a right angle and is obtuse and is acute and is a right triangle. and is an obtuse triangle is an a acute triangle Theorem: If the square of the longest side of a triangle is greater than the sum of the squares of the other two sides, then the triangle is an obtuse triangle. Theorem: If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is an acute triangle. c a b a c b c a b Note: Remember to check if it is a. irections: If a triangle is formed with the given lengths, is it acute, right, or obtuse? 5. 8, 9, , 5, , 13, , 7, , 2 3, , 11, , 5, , 5, 5 3
7 8.4 Special Right Triangles Two special Types: I Solve: II () Solve: 3 2( ) III. Solve for
8 84 Special Right ngles (ay 2) So why does it work I hyp. 45 II long 30 hyp short III Solve:
9 IV () Solve: 3 2()
10 8.5 The Tangent Ratio Trigonometric Functions S  Sine O opp H hyp osine adj H hyp T Tangent O opp  adj opp. adj. adj. opp. hyp. hyp. Today we deal with Tangent(TO) I. Epress tan X and tan Y as ratios. 1. Z 2. Y X Z X Y Y X Z Y Z 20 X Refer to the Table of Trigonometric Ratios on pg. 311 of your tetbook. 5. tan tan tan tan tan tan
11 II. Find the value of to the nearest tenth freeway ramp has a 10% grade. What 17 angle does the ramp have with the ground? y 8 rise 200 [Note: Grade(%) = *100 ] run 60 z
12 8.6 The Sine and osine Ratios Trigonometric Functions S  Sine O opp H hyp osine adj H hyp T Tangent O opp  adj opp. adj. Today we deal with SOH and H adj. opp. hyp. hyp. I. Epress Sin, Sin, os and os as ratios
13 II. Find the value of and y to the nearest tenth y y 15. y y n n n 5
14 87 pplications of Right Triangles I. Terms To Know: ngle of Elevation ngle of epression II. The Problems 1. From a point 80m from the base of a tower, the of elevation to the top of the tower is 28 o. How tall is the tower? 2. ladder that is 20ft. is leaning against the side of a building. If the formed between the ladder and the ground is 75 o, how far is the bottom of the ladder from the base of the building? 3. When the sun is 62 o above the horizon, a building casts a shadow 18m long. How tall is the building? 4. kite is flying at an of elevation of about 55 o. Ignoring the sag in the string, find the height of the kite if 85m of string have been let out.
15 5. wire is attached to the top of a tower and to a point on the ground that is 35m from the base of the tower. If the wire makes a 65 o angle with the ground, how long is the wire? 6. The angle of depression from the top of a tower to a boulder on the ground is 38 o. If the tower is 25m high, how far from the base of tower is the boulder? 7. n observer at the top of a building sees a car on the road below. The of depression to the car is 28 o. If the car is about 50m from the building when it is seen, how tall is the building?
Squares and Square Roots Algebra 11.1
Squares and Square Roots Algebra 11.1 To square a number, multiply the number by itself. Practice: Solve. 1. 1. 0.6. (9) 4. 10 11 Squares and Square Roots are Inverse Operations. If =y then is a square
More informationChapter 2: Pythagoras Theorem and Trigonometry (Revision)
Chapter 2: Pythagoras Theorem and Trigonometry (Revision) Paper 1 & 2B 2A 3.1.3 Triangles Understand a proof of Pythagoras Theorem. Understand the converse of Pythagoras Theorem. Use Pythagoras 3.1.3 Triangles
More information5/6 Lesson: Angles, measurement, right triangle trig, and Pythagorean theorem
5/6 Lesson: Angles, measurement, right triangle trig, and Pythagorean theorem I. Lesson Objectives: Students will be able to recall definitions of angles, how to measure angles, and measurement systems
More informationChapter 8 Practice Test
Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In triangle ABC, is a right angle and 45. Find BC. If you answer is not an integer,
More information13.4 Chapter 13: Trigonometric Ratios and Functions. Section 13.4
13.4 Chapter 13: Trigonometric Ratios and Functions Section 13.4 1 13.4 Chapter 13: Trigonometric Ratios and Functions Section 13.4 2 Key Concept Section 13.4 3 Key Concept Section 13.4 4 Key Concept Section
More informationThe reciprocal identities are obvious from the definitions of the six trigonometric functions.
The Fundamental Identities: (1) The reciprocal identities: csc = 1 sec = 1 (2) The tangent and cotangent identities: tan = cot = cot = 1 tan (3) The Pythagorean identities: sin 2 + cos 2 =1 1+ tan 2 =
More informationSpecial Right Triangles and Right Triangle Trigonometry
Special Right Triangles and Right Triangle Trigonometry Reporting Category Topic Triangles Investigating special right triangles and right triangle trigonometry Primary SOL G.8 The student will solve realworld
More informationUsing Trigonometric Ratios Part 1: Solving For Unknown Sides
MPM2D: Principles of Mathematics Using Trigonometric Ratios Part 1: Solving For Unknown Sides J. Garvin Slide 1/15 Recap State the three primary trigonometric ratios for A in ABC. Slide 2/15 Recap State
More informationcos sin sin 2 60 = 1.
Name: Class: Date: Use the definitions to evaluate the six trigonometric functions of. In cases in which a radical occurs in a denominator, rationalize the denominator. Suppose that ABC is a right triangle
More informationDate: Worksheet 48: Problem Solving with Trigonometry
Worksheet 48: Problem Solving with Trigonometry Step 1: Read the question carefully. Pay attention to special terminology. Step 2: Draw a triangle to illustrate the situation. Decide on whether the triangle
More informationUnit 5. Algebra 2. Name:
Unit 5 Algebra 2 Name: 12.1 Day 1: Trigonometric Functions in Right Triangles Vocabulary, Main Topics, and Questions Definitions, Diagrams and Examples Theta Opposite Side of an Angle Adjacent Side of
More informationName: A Trigonometric Review June 2012
Name: A Trigonometric Review June 202 This homework will prepare you for inclass work tomorrow on describing oscillations. If you need help, there are several resources: tutoring on the third floor of
More informationAreas of Tropezoids, Rhombuses, and Kites
102 Areas of Tropezoids, Rhombuses, and Kites MathemaHcs Florida Standards MAFS.912.GMG.1.1 Use geometric shapes, their measures, and their properties to describe objects. MP1. MP3, MP 4,MP6 Objective
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 1316 Ch.12 Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Find the supplement of an angle whose
More informationSquare Roots and the Pythagorean Theorem
UNIT 1 Square Roots and the Pythagorean Theorem Just for Fun What Do You Notice? Follow the steps. An example is given. Example 1. Pick a 4digit number with different digits. 3078 2. Find the greatest
More informationDate: Period: Quadrilateral Word Problems: Review Sheet
Name: Quadrilateral Word Problems: Review Sheet Date: Period: Geometry Honors Directions: Please answer the following on a separate sheet of paper. Completing this review sheet will help you to do well
More information1. 1 Square Numbers and Area Models (pp. 610)
Math 8 Unit 1 Notes Name: 1. 1 Square Numbers and Area Models (pp. 610) square number: the product of a number multiplied by itself; for example, 25 is the square of 5 perfect square: a number that is
More informationGeometry by Jurgensen, Brown and Jurgensen Postulates and Theorems from Chapter 1
Postulates and Theorems from Chapter 1 Postulate 1: The Ruler Postulate 1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. 2. Once
More informationLesson 27: Sine and Cosine of Complementary and Special Angles
Lesson 7 M Classwork Example 1 If α and β are the measurements of complementary angles, then we are going to show that sin α = cos β. In right triangle ABC, the measurement of acute angle A is denoted
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation.
More informationMod E  Trigonometry. Wednesday, July 27, M132Blank NotesMOM Page 1
M132Blank NotesMOM Page 1 Mod E  Trigonometry Wednesday, July 27, 2016 12:13 PM E.0. Circles E.1. Angles E.2. Right Triangle Trigonometry E.3. Points on Circles Using Sine and Cosine E.4. The Other Trigonometric
More informationGAP CLOSING. Powers and Roots. Intermediate / Senior Student Book GAP CLOSING. Powers and Roots. Intermediate / Senior Student Book
GAP CLOSING Powers and Roots GAP CLOSING Powers and Roots Intermediate / Senior Student Book Intermediate / Senior Student Book Powers and Roots Diagnostic...3 Perfect Squares and Square Roots...6 Powers...
More informationTrigonometry Review Page 1 of 14
Trigonometry Review Page of 4 Appendix D has a trigonometric review. This material is meant to outline some of the proofs of identities, help you remember the values of the trig functions at special values,
More informationNumbers & Operations Chapter Problems
Numbers & Operations 8 th Grade Chapter Questions 1. What are the properties of a square? 2. What does taking the square root have to do with the area of a square? 3. Why is it helpful to memorize perfect
More informationJune 2016 Regents GEOMETRY COMMON CORE
1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which threedimensional object below is generated by this rotation? 4) 2
More informationMath Problem Set 5. Name: Neal Nelson. Show Scored View #1 Points possible: 1. Total attempts: 2
Math Problem Set 5 Show Scored View #1 Points possible: 1. Total attempts: (a) The angle between 0 and 60 that is coterminal with the 69 angle is degrees. (b) The angle between 0 and 60 that is coterminal
More informationChapter 11 Trigonometric Ratios The Sine Ratio
Chapter 11 Trigonometric Ratios 11.2 The Sine Ratio Introduction The figure below shows a rightangled triangle ABC, where B = and C = 90. A hypotenuse B θ adjacent side of opposite side of C AB is called
More informationChapter 1 and Section 2.1
Chapter 1 and Section 2.1 Diana Pell Section 1.1: Angles, Degrees, and Special Triangles Angles Degree Measure Angles that measure 90 are called right angles. Angles that measure between 0 and 90 are called
More informationh r c On the ACT, remember that diagrams are usually drawn to scale, so you can always eyeball to determine measurements if you get stuck.
ACT Plane Geometry Review Let s first take a look at the common formulas you need for the ACT. Then we ll review the rules for the tested shapes. There are also some practice problems at the end of this
More informationRight Triangle Trigonometry (Section 43)
Right Triangle Trigonometry (Section 43) Essential Question: How does the Pythagorean Theorem apply to right triangle trigonometry? Students will write a summary describing the relationship between the
More informationName Date. Chapter 15 Final Review
Name Date Chapter 15 Final Review Tell whether the events are independent or dependent. Explain. 9) You spin a spinner twice. First Spin: You spin a 2. Second Spin: You spin an odd number. 10) Your committee
More informationSemester 1 Final Exam Review
Target 1: Vocabulary and notation Semester 1 Final Exam Review Name 1. Find the intersection of MN and LO. 2. 3) Vocabulary: Define the following terms and draw a diagram to match: a) Point b) Line c)
More informationAssignment 5 unit34radicals. Due: Friday January 13 BEFORE HOMEROOM
Assignment 5 unit34radicals Name: Due: Friday January 13 BEFORE HOMEROOM Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the prime factorization
More informationGEO: Sem 1 Unit 1 Review of Geometry on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1)
GEO: Sem 1 Unit 1 Review of Geometr on the Coordinate Plane Section 1.6: Midpoint and Distance in the Coordinate Plane (1) NAME OJECTIVES: WARM UP Develop and appl the formula for midpoint. Use the Distance
More informationTERRA Environmental Research Institute
TERRA Environmental Research Institute MATHEMATICS FCAT PRACTICE STRAND 3 Geometry and Spatial Sense Angle Relationships Lines and Transversals Plane Figures The Pythagorean Theorem The Coordinate Plane
More informationRoots and Radicals Chapter Questions
Roots and Radicals Chapter Questions 1. What are the properties of a square? 2. What does taking the square root have to do with the area of a square? 3. Why is it helpful to memorize perfect squares?
More informationGeometer s Skethchpad 8th Grade Guide to Learning Geometry
Geometer s Skethchpad 8th Grade Guide to Learning Geometry This Guide Belongs to: Date: Table of Contents Using Sketchpad                                        
More informationHow to Do Trigonometry Without Memorizing (Almost) Anything
How to Do Trigonometry Without Memorizing (Almost) Anything Moti enari Weizmann Institute of Science http://www.weizmann.ac.il/scitea/benari/ c 07 by Moti enari. This work is licensed under the reative
More informationFigure 1. The unit circle.
TRIGONOMETRY PRIMER This document will introduce (or reintroduce) the concept of trigonometric functions. These functions (and their derivatives) are related to properties of the circle and have many interesting
More informationName. Ms. Nong. Due on: Per: Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0
Name FRIDAY, FEBRUARY 24 Due on: Per: TH Geometry 2 nd semester Math packet # 2 Standards: 8.0 and 16.0 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume
More informationStudents apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.
Student Outcomes Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions. Lesson Notes It is recommended that students have access to a calculator as they work
More informationMathematics Lecture. 3 Chapter. 1 Trigonometric Functions. By Dr. Mohammed Ramidh
Mathematics Lecture. 3 Chapter. 1 Trigonometric Functions By Dr. Mohammed Ramidh Trigonometric Functions This section reviews the basic trigonometric functions. Trigonometric functions are important because
More information3 Kevin s work for deriving the equation of a circle is shown below.
June 2016 1. A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which threedimensional object below is generated by this rotation?
More informationTrigonometry Review Tutorial Shorter Version
Author: Michael MigdailSmith Originally developed: 007 Last updated: June 4, 0 Tutorial Shorter Version Avery Point Academic Center Trigonometric Functions The unit circle. Radians vs. Degrees Computing
More informationConstructions. Learning Intention: By If you use 1 litre of orange, you will use 4 litres of water (1:4).
Constructions Scales Scales are important in everyday life. We use scales to draw maps, to construct building plans, in housing, street construction... It is impossible to draw building plans with the
More informationPythagorean Theorem. 2.1 Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem... 45
Pythagorean Theorem What is the distance from the Earth to the Moon? Don't let drawings or even photos fool you. A lot of them can be misleading, making the Moon appear closer than it really is, which
More informationUNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet
Name Period Date UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet 24.1 The Pythagorean Theorem Explore the Pythagorean theorem numerically, algebraically, and geometrically. Understand a proof
More informationLesson 6.1 Skills Practice
Lesson 6.1 Skills Practice Name Date Soon You Will Determine the Right Triangle Connection The Pythagorean Theorem Vocabulary Match each definition to its corresponding term. 1. A mathematical statement
More informationModule Guidance Document. Geometry Module 2
Geometry Module 2 Topic A Scale Drawings 5 days Topic B Dilations 5 days Topic C Similarity and Dilations 15 days Topic D Applying Similarity to Right 7 days Triangles Topic D Trigonometry 13 days Just
More informationIndicate whether the statement is true or false.
MATH 121 SPRING 2017  PRACTICE FINAL EXAM Indicate whether the statement is true or false. 1. Given that point P is the midpoint of both and, it follows that. 2. If, then. 3. In a circle (or congruent
More informationPythagorean Theorem: Trigonometry Packet #1 S O H C A H T O A. Examples Evaluate the six trig functions of the angle θ. 1.) 2.)
Trigonometry Packet #1 opposite side hypotenuse Name: Objectives: Students will be able to solve triangles using trig ratios and find trig ratios of a given angle. S O H C A H T O A adjacent side θ Right
More informationDownloaded from
1 IX Mathematics Chapter 8: Quadrilaterals Chapter Notes Top Definitions 1. A quadrilateral is a closed figure obtained by joining four points (with no three points collinear) in an order. 2. A diagonal
More informationUniversity of Houston High School Mathematics Contest Geometry Exam Spring 2016
University of Houston High School Mathematics ontest Geometry Exam Spring 016 nswer the following. Note that diagrams may not be drawn to scale. 1. In the figure below, E, =, = 4 and E = 0. Find the length
More informationThe City School. Comprehensive Worksheet (1st Term) November 2018 Mathematics Class 8
The City School Comprehensive Worksheet (1st Term) November 2018 Mathematics Class 8 Index No: S i INSTRUCTIONS Write your index number, section, school/campus and date clearly in the space provided Read
More informationMathematical Construction
Mathematical Construction Full illustrated instructions for the two bisectors: Perpendicular bisector Angle bisector Full illustrated instructions for the three triangles: ASA SAS SSS Note: These documents
More informationBook 10: Slope & Elevation
Math 21 Home Book 10: Slope & Elevation Name: Start Date: Completion Date: Year Overview: Earning and Spending Money Home Travel and Transportation Recreation and Wellness 1. Budget 2. Personal Banking
More informationCatty Corner. Side Lengths in Two and. Three Dimensions
Catty Corner Side Lengths in Two and 4 Three Dimensions WARM UP A 1. Imagine that the rectangular solid is a room. An ant is on the floor situated at point A. Describe the shortest path the ant can crawl
More information4.2 Proving and Applying
YOU WILL NEED alulator ruler EXPLORE 4.2 Proving and Applying the Sine and Cosine Laws for Obtuse Triangles An isoseles obtuse triangle has one angle that measures 120 and one side length that is 5 m.
More informationE G 2 3. MATH 1012 Section 8.1 Basic Geometric Terms Bland
MATH 1012 Section 8.1 Basic Geometric Terms Bland Point A point is a location in space. It has no length or width. A point is represented by a dot and is named by writing a capital letter next to the dot.
More informationPreCalculus 4/10/13 Obj: Midterm Review
PreCalculus 4/10/13 Obj: Midterm Review Agenda 1. Bell Ringer: None 2. #35, 72 Parking lot 37, 39, 41 3. Homework Requests: Few minutes on Worksheet 4. Exit Ticket: In Class Exam Review Homework: Study
More informationProject Maths Geometry Notes
The areas that you need to study are: Project Maths Geometry Notes (i) Geometry Terms: (ii) Theorems: (iii) Constructions: (iv) Enlargements: Axiom, theorem, proof, corollary, converse, implies The exam
More informationRepresenting Square Numbers. Use materials to represent square numbers. A. Calculate the number of counters in this square array.
1.1 Student book page 4 Representing Square Numbers You will need counters a calculator Use materials to represent square numbers. A. Calculate the number of counters in this square array. 5 5 25 number
More informationAnalytic Geometry EOC Study Booklet Geometry Domain Units 13 & 6
DOE Assessment Guide Questions (2015) Analytic Geometry EOC Study Booklet Geometry Domain Units 13 & 6 Question Example Item #1 Which transformation of ΔMNO results in a congruent triangle? Answer Example
More informationACCELERATED MATHEMATICS CHAPTER 14 PYTHAGOREAN THEOREM TOPICS COVERED: Simplifying Radicals Pythagorean Theorem Distance formula
ACCELERATED MATHEMATICS CHAPTER 14 PYTHAGOREAN THEOREM TOPICS COVERED: Simplifying Radicals Pythagorean Theorem Distance formula Activity 141: Simplifying Radicals In this chapter, radicals are going
More informationLesson: Pythagorean Theorem Lesson Topic: Use Pythagorean theorem to calculate the hypotenuse
Lesson: Pythagorean Theorem Lesson Topic: Use Pythagorean theorem to calculate the hypotenuse Question 1: What is the length of the hypotenuse? ft Question 2: What is the length of the hypotenuse? m Question
More informationFINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true.
FINL RVIW 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram. c) oth
More informationGeometry Mrs. Crocker Spring 2014 Final Exam Review
Name: Mod: Geometry Mrs. Crocker Spring 2014 Final Exam Review Use this exam review to complete your flip book and to study for your upcoming exam. You must bring with you to the exam: 1. Pencil, eraser,
More informationB. Examples: 1. At NVHS, there are 104 teachers and 2204 students. What is the approximate teacher to student ratio?
Name Date Period Notes Formal Geometry Chapter 7 Similar Polygons 7.1 Ratios and Proportions A. Definitions: 1. Ratio: 2. Proportion: 3. Cross Products Property: 4. Equivalent Proportions: B. Examples:
More informationStudent Instruction Sheet: Unit 4 Lesson 1. Pythagorean Theorem
Student Instruction Sheet: Unit 4 Lesson 1 Suggested time: 75 minutes Pythagorean Theorem What s important in this lesson: In this lesson you will learn the Pythagorean Theorem and how to apply the theorem
More information6.00 Trigonometry Geometry/Circles Basics for the ACT. Name Period Date
6.00 Trigonometry Geometry/Circles Basics for the ACT Name Period Date Perimeter and Area of Triangles and Rectangles The perimeter is the continuous line forming the boundary of a closed geometric figure.
More informationGeometry 1 FINAL REVIEW 2011
Geometry 1 FINL RVIW 2011 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram.
More informationStudent Name: Teacher: Date: District: Rowan. Assessment: 9_12 T and I IC61  Drafting I Test 1. Form: 501
Student Name: Teacher: Date: District: Rowan Assessment: 9_12 T and I IC61  Drafting I Test 1 Description: Test 4 A (Diagrams) Form: 501 Please use the following figure for this question. 1. In the GEOMETRIC
More informationDay 1. Last Night s Homework Angle Worksheet (11 problems) Bellwork Angle quiz.
Course: 7 th Grade Math DETAIL LESSON PLAN Wednesday, January 25 / Thursday, January 26 Student Objective (Obj. 3e) TSW use the Pythagorean Theorem to find the missing length of a side of a right triangle.
More informationll6 The Pythagorean Theorem
ll6 The Pythagorean Theorem Objective To use the Pythagorean theorem and its converse to solve geometric problems. The Pythagorean theorem can be used to find the lengths of sides of right triangles.
More informationClass 5 Geometry O B A C. Answer the questions. For more such worksheets visit
ID : in5geometry [1] Class 5 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) The set square is in the shape of. (2) Identify the semicircle that contains 'C'. A C O B
More informationTrigonometry: A Brief Conversation
Cit Universit of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Communit College 018 Trigonometr: A Brief Conversation Caroln D. King PhD CUNY Queensborough Communit College
More informationMHR Foundations for College Mathematics 11 Solutions 1. Chapter 1 Prerequisite Skills. Chapter 1 Prerequisite Skills Question 1 Page 4 = 6+ =
Chapter 1 Trigonometry Chapter 1 Prerequisite Skills Chapter 1 Prerequisite Skills Question 1 Page 4 a) x 36 b) x 6 19 x ± 36 x ± 6 x x 6+ 19 5 x ± 5 x ± 5 c) x 64 + 36 d) x 5 + 1 x 100 x 5 + 144 x ± 100
More informationc) What is the ratio of the length of the side of a square to the length of its diagonal? Is this ratio the same for all squares? Why or why not?
Tennessee Department of Education Task: Ratios, Proportions, and Similar Figures 1. a) Each of the following figures is a square. Calculate the length of each diagonal. Do not round your answer. Geometry/Core
More information1999 Mathcounts National Sprint Round Solutions
999 Mathcounts National Sprint Round Solutions. Solution: 5. A digit number is divisible by if the sum of its digits is divisible by. The first digit cannot be 0, so we have the following four groups
More informationLesson 3.1 Duplicating Segments and Angles
Lesson 3.1 Duplicating Segments and ngles Name eriod Date In Exercises 1 3, use the segments and angles below. omplete the constructions on a separate piece of paper. S 1. Using only a compass and straightedge,
More informationMeet #5 March Intermediate Mathematics League of Eastern Massachusetts
Meet #5 March 2008 Intermediate Mathematics League of Eastern Massachusetts Meet #5 March 2008 Category 1 Mystery 1. In the diagram to the right, each nonoverlapping section of the large rectangle is
More information13.2 Define General Angles and Use Radian Measure. standard position:
3.2 Define General Angles and Use Radian Measure standard position: Examples: Draw an angle with the given measure in standard position..) 240 o 2.) 500 o 3.) 50 o Apr 7 9:55 AM coterminal angles: Examples:
More informationHow can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr.
Common Core Standard: 8.G.6, 8.G.7 How can we organize our data? What other combinations can we make? What do we expect will happen? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.2.2 What Is Special
More information1. Convert 60 mi per hour into km per sec. 2. Convert 3000 square inches into square yards.
ACT Practice Name Geo Unit 3 Review Hour Date Topics: Unit Conversions Length and Area Compound shapes Removing Area Area and Perimeter with radicals Isosceles and Equilateral triangles Pythagorean Theorem
More informationC.3 Review of Trigonometric Functions
C. Review of Trigonometric Functions C7 C. Review of Trigonometric Functions Describe angles and use degree measure. Use radian measure. Understand the definitions of the si trigonometric functions. Evaluate
More informationD.3. Angles and Degree Measure. Review of Trigonometric Functions
APPENDIX D. Review of Trigonometric Functions D7 APPENDIX D. Review of Trigonometric Functions Angles and Degree Measure Radian Measure The Trigonometric Functions Evaluating Trigonometric Functions Solving
More information(A) Circle (B) Polygon (C) Line segment (D) None of them (A) (B) (C) (D) (A) Understanding Quadrilaterals <1M>
Understanding Quadrilaterals 1.A simple closed curve made up of only line segments is called a (A) Circle (B) Polygon (C) Line segment (D) None of them 2.In the following figure, which of the polygon
More informationWorksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics
Worksheet 10 Memorandum: Construction of Geometric Figures Grade 9 Mathematics For each of the answers below, we give the steps to complete the task given. We ve used the following resources if you would
More information3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm.
1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More informationGeometry  Chapter 6 Review
Class: Date: Geometry  Chapter 6 Review 1. Find the sum of the measures of the angles of the figure. 4. Find the value of x. The diagram is not to scale. A. 1260 B. 900 C. 540 D. 720 2. The sum of the
More informationPart I Multiple Choice
Oregon Focus on Lines and Angles Block 3 Practice Test ~ The Pythagorean Theorem Name Period Date Long/Short Term Learning Targets MA.MS.08.ALT.05: I can understand and apply the Pythagorean Theorem. MA.MS.08.AST.05.1:
More informationStudent s Copy. Geometry Unit 2. Similarity, Proof, and Trigonometry. Eureka Math. Eureka Math
Student s Copy Geometry Unit 2 Similarity, Proof, and Trigonometry Eureka Math Eureka Math Lesson 1 Lesson 1: Scale Drawings Triangle AAAAAA is provided below, and one side of scale drawing AA BB CC is
More information9.5 Properties and Conditions for Kites and Trapezoids
Name lass ate 9.5 Properties and onditions for Kites and Trapezoids ssential uestion: What are the properties of kites and trapezoids? Resource Locker xplore xploring Properties of Kites kite is a quadrilateral
More informationTrigonometric identities
Trigonometric identities An identity is an equation that is satisfied by all the values of the variable(s) in the equation. For example, the equation (1 + x) = 1 + x + x is an identity. If you replace
More information(A) Circle (B) Polygon (C) Line segment (D) None of them
Understanding Quadrilaterals 1.The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60 degree. Find the angles of the parallelogram.
More information7.1 INTRODUCTION TO PERIODIC FUNCTIONS
7.1 INTRODUCTION TO PERIODIC FUNCTIONS *SECTION: 6.1 DCP List: periodic functions period midline amplitude Pg 247 LECTURE EXAMPLES: Ferris wheel, 14,16,20, eplain 23, 28, 32 *SECTION: 6.2 DCP List: unit
More informationThe area A of a trapezoid is one half the product of the height h and the sum of the lengths of its bases, b 1 and b 2.
ALGEBRA Find each missing length. 21. A trapezoid has a height of 8 meters, a base length of 12 meters, and an area of 64 square meters. What is the length of the other base? The area A of a trapezoid
More information2. Here are some triangles. (a) Write down the letter of the triangle that is. rightangled, ... (ii) isosceles. ... (2)
Topic 8 Shapes 2. Here are some triangles. A B C D F E G (a) Write down the letter of the triangle that is (i) rightangled,... (ii) isosceles.... (2) Two of the triangles are congruent. (b) Write down
More informationThe Pythagorean Theorem 8.6.C
? LESSON 8.1 The Pythagorean Theorem ESSENTIAL QUESTION Expressions, equations, and relationships 8.6.C Use models and diagrams to explain the Pythagorean Theorem. 8.7.C Use the Pythagorean Theorem...
More informationGAP CLOSING. Powers and Roots. Intermediate / Senior Facilitator Guide
GAP CLOSING Powers and Roots Intermediate / Senior Facilitator Guide Powers and Roots Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5 Solutions...5
More information