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 Transformations Similar Figures Right Triangle Trigonometry SUNSHINE STATE STANDARDS AND BENCHMARKS MA.B.1.4.1 MA.C.1.3.1 MA.C.2.4.1 MA.C.3.4.1 MA.C.3.4.2
TIPS A straight angle measures 180. A straight angle forms a straight line. A right angle measures 90. A right angle is usually marked with a little square at the vertex. An acute angle measures more than 0 and less than 90 An obtuse angle measures more than 90 and less than 180. A reflex angle measures more than 180. Two angles are supplementary if their sum equals 180. Two angles are complementary if their sum equals 90. The sum of the angles of any triangle is always 180. The sum of the angles of any quadrilateral is always 360. To bisect means to divide into two equal parts. Adjacent means next to. When two parallel lines are cut by a transversal the following angles are formed. Alternate Interior Angles are always congruent. 3 6 and 4 5 Alternate Exterior Angles are always congruent. 1 8 and 2 7 Corresponding Angles are always congruent. 1 5, 3 7, 2 6, 4 8 Vertical Angles are congruent. In the figure above 1 and 4 are vertical angles. Can you find more? Perpendicular lines are lines which intersect forming 90 angles. The Pythagorean Theorem: a 2 + b 2 = c 2 only applies to right triangles, where a and b are the lengths of the legs and c is the length of the hypotenuse. An Isosceles Triangle has two sides of equal length. An Equilateral Triangle has all three sides of equal length. There are three types of transformations: Translation (slide), Reflection (flip) and Rotation (Turn) Two figures are similar if their corresponding angles are congruent and their corresponding sides are in proportion. Right Triangle Trigonometry: sin x opp cos x hyp adj tan x hyp Add your own notes as we practice with the following problems. opp (SOHCAHTOA) adj 1
FCAT PRACTICE STRAND 3 Student Name Date Current Math Teacher 1) A ceiling fan with five equally-spaced blades is shown below. What is the degree measure of x? A. 36 C. 108 B. 72 D. 144 2) In the figure at the right, the letter F is to be first reflected over the vertical line m and then again reflected over the horizontal line p. Which of the figures below would be the correct orientation of the letter F after the two transformations described? 3) Al was taking a tour of the Kennedy Space Center. He could see a space shuttle being prepared for launch a distance, d, away. He held one of his keys out at arm s length and noticed that, at this distance, the shuttle appeared to be about the same size as his key. Al knows that the shuttle is really about 120 feet in length and that his key is about 2 inches long. He is holding the key 24 inches away from his eyes. Using this information, which is closest to the distance, d, between Al and the space shuttle? A. 240 feet C. 2880 feet B. 1440 feet D. 5760 feet 2
4) The diagram below shows a design found on a mask from Nigeria. In the diagram, ACB measures 134, and ACD measures 128. What is the measure, in degrees, of BCD? 5) Rita designs and tests model rockets. She made a device that allows her to measure the angle of the rocket s elevation at the peak of its path. During one test, she used the device at a point 60 feet from the launch pad. When the rocket reached the peak of its path, the measurements on Rita s device were as shown in the diagram below: Based on Rita s measurements, what was the approximate height, in feet, that the rocket reached at the peak of its path? A) 48 feet C) 96 feet B) 75 feet D) 128 feet 6) The dimensions and shape of a volley-ball court are shown in this picture. What is the approximate distance of a serve that is hit diagonally from one corner of the court to the other? A) 27 meters C) 15.6 meters B) 20.1 meters D) 12.7 meters 3
7) An architect is using isosceles triangles in the design of a bridge. In the diagram below, all line segments represent the steel beams needed to build this section of the bridge. Line segment HA is parallel to line segment DB. DEC is similar to CAB and congruent to AFG. Part A: Write and solve a proportion to determine the length, in feet, of EC. Show your work. Part B: In the diagram, all the smaller triangles are congruent, and all the larger triangles are congruent. Determine the total length, in feet, of all the steel beams needed to build the section of the bridge shown. Show all the work needed to determine the total length of the beams. 8) The wing of a paper airplane is in the shape shown. If B measures 152, what is the measure of A? A) 23 C) 51 B) 28 D) 54 9) A contractor needs to know the width of a pond. She makes the measurements shown below. Which of the proportions could be used to find the width (w) of the pond? A) 20 w C) w 46 57 57 B) 20 w D) w 46 103 20 67 103 57 46 10) Lance has drawn the following logo for his new business. The three horizontal lines on the logo are parallel. The measure of one angle is marked. What is the value of x? A) 28 C) 118 B) 62 D) Not enough information given. 11) Which choice describes the transformation of figure CDE shown? A) rotation 180 about point C. B) dilation with a scale factor of 2. C) translation 2 units to the right D) reflection over the y-axis. 4
12) When artists draw a female figure like the one in this picture, the realistic ratio of the distance from the hip to the toe (x) to the height of the woman (y) is 0.613. An artist is creating a 9-inch high drawing of a woman. What should be the approximate distance in inches from the hip to the toe? A) 0.07 inch C) 5.5 inches B) 3.5 inches D) 14.7 inches. 13) One side of isosceles triangle PQR is drawn on the coordinate plane on the right. If PQ QR and PR is parallel to the x-axis, what are the coordinates of point R? A) (2, -3) C) (4, -1) B) (3, -3) D) (4, -3) 14) Use the figure to find the value of x. 15) A path passes between two flower beds. BI has been added to the drawing such that BI AC. What is the measure of the smallest angle of the triangular bed, ACD? 5
16) In the figure to the right, AE FI. Find the measure of the following angles: a) BCD b) KHG c) HGJ d) BCA 17) The building below is 76 meters in height. The angle of the line of sight from the top of the building to the foot of the second building is shown in the drawing. What is the distance between the buildings, rounded to the nearest meter? sin 42 0.669 cos 42 0.743 tan 42 0.900 18) A surveyor stands 160 feet from the base of a tall tree. The height of the tree is shown in the drawing. Which on the following equations could be used to find the angle of elevation? A. tan B = 80 160 B. cos A = 80 160 C. tan A = 160 80 D. sin B = 160 80 19) Two angles of BCD measure 36 and 46. What kind of triangle is BCD? A. right triangle B. obtuse triangle C. acute triangle D. equilateral triangle 20) The legs of a right triangle measure 0.75 inch and 1 inch. What is the measure of the hypotenuse? A. 0.625 B. 1.25 C. 1.5625 D. 1.75 6
FCAT PRACTICE STRAND 3 - ANSWER SHEET Student Name Date Current Math Teacher: 1) A B C D 2) A B C D 3) A B C D 4) 5) A B C D 6) A B C D 7a) Answer: b) Answer: 8) A B C D 9) A B C D 10) A B C D 11) A B C D 12) A B C D 13) A B C D 14) 15) 16) 17) a) BCD b) KHG c) HGJ d) BCA 18) A B C D 19) A B C D 20) A B C D 7