Geometry Final Exam Review 2012 #

Transcription

1 1 PART 1: Multiple Choice (40 x 2 points = 80%). PART 2: Open Ended (2 x 10 = 20%) 1) Find the volume and surface area of the following rectangular prisms 2) Find the surface area of the following cylinders. 3) The area of a triangle is 150 sq. ft. The height is 10 ft. What is the length of the base? a) 30 ft b) 12 ft c) 6 ft. d) 18 ft. 4) List the sides in order from shortest to longest 5) The area of a triangle is 150 sq. ft. The height is 15 ft. What is the length of the base? 6) How tall is the tree, if the ladder is 12 ft long?

2 2 7) How high is the monument? 8) ABCD is a rectangle. Find x, if AC = -5x +6 and BD = -x ) ABCD is a rectangle. Find m<12 and m<11 respectively, if m<9 = ) Use trapezoid ABCD. Find x, if MN = x + 10, AB = 4x - 2, and CD = 2x ) ABC ~ XYZ, find perimeter of XYZ.

3 3 12) The area of the circle is 50.1 in 2. Find the circumference of the circle. Round your answer to the nearest tenth. 13) The circumference of the circle is 13.1 in. Find the area of the circle. Round your answer to the nearest tenth. 14) Find missing dimension of a triangle: 15) Find the measure of each side of a square: If A = A) 5.8 in B) 7.9 in C) 8.4 in D) none 16) Name Postulate, if possible. 17) Name Postulate, if possible.

4 4 18) Which postulate if any would make these triangles congruent? 19) Find an area and perimeter of the square below. 20) Use isosceles trapezoid ABCD. Find m<d, m<a and m<c respectively, if m<b = ) Use trapezoid ABCD. Find x, if MN = 2x + 24, AB = 3x + 2, and CD = 7x ) Find BC if AD is an altitude of ABC

5 5 23) Find m<abc if BD is an angle bisector of ABC 24) Which of the following CANNOT be the possible lengths of the sides of a right triangle? a) 3, 4, 5 b) 1, 1, 2 c) 5, 12, 13 d) 6, 8, 10 25) In isosceles triangle KLM, angle M is the vertex angle. Find the measure of angle K, if angle M is 62 degrees. 26) Find the measure of angle BCA 27) Quadrilateral ABCD is similar to Quadrilateral RSTU. Find X.

6 6 Use parallelogram RSTU to answer questions ) If m<rst = x + 20 and m<stu = 2x+ 10, find m<rst 29) If ST= 2x + 10 and RU= 5x 2, find ST 30) If SV = 2x + 6 and SU = 24, find the value of x 31) Triangle ABC can be classified as 32) A boat is traveling 25 miles due east from a harbor, then turns and sails 7 miles due south. How far is the boat from the harbor? Round your answer to the nearest whole number 33) Find x if possible, if impossible say so. 34) Find x if possible, if impossible say so.

7 7 35) Name the biggest and the smallest angle in a triangle, if possible. 36) Determine whether it is possible to draw a triangle with the given measures: 6 in, 2 in, and 4 in. 37) The two sides of a triangle are: 10, 4. Between what two numbers must the measure of the third side of a triangle fall? 38) An escalator is 30 feet long with a 250 incline. How high is the escalator? 39) An airplane rises 800 ft vertically over a horizontal distance of 500 ft. What is the angle of elevation? See next page for Part 2- Open Ended

8 8 Part 2: Open Ended (use graph paper) MUST PICK ONLY 2 Extra Credit given for a third one. (2 x 10% = 20%) Open-Ended Question #1: 1) Given right triangle ABC. a) Find midpoints of sides AB and AC, label them X and Y accordingly. Find measures of all sides of ABC and AXY. Show your work. b) Find perimeters of ABC and AXY. What is the ratio of perimeter of AXY to perimeter of ABC? Show your work. c) Find areas of ABC and AXY. What is the ratio of area of ABC to area of AXY? Show your work. d) Find area of quadrilateral XYCB. What is the ratio of area of AXY to area of quadrilateral XYCB? Show your work.

9 9 Open Ended #2 2) Sam is making a fenced area for his dog. He has 20 feet of fencing left over from another project. a) Draw all possible rectangular areas that can be made using entire fencing, Label the sides. b) Find the area of each rectangle. Which has the greatest area? c) If Sam uses a circle for the dog run area, what will it diameter be? Draw a circle, label it. Find its area. Compare its area with the areas of the rest of the rectangles. d) What shape will Sam decide to make the dog run to have the greatest possible area. Explain. Open Ended #3 The building with the floor plan was built at a cost of $22.50 per square the reproduction cost today is $91,584, foot. If a) Find the cost of the building when it was first designed. b) Find the cost per square foot at the reproduction cost. c) Find the percent of increase in square footage costs ft. 28 ft. 84 ft. Open Ended #4 Mike travels north to the store 8 blocks then travels west 6 blocks to the library. a) Draw a vector diagram to represent this situation b) What would be the longest route to travel? Show your work and explain your answer. c) What would be the shortest route for Michael to travel from home to the library? Show your work and explain your answer.

10 10 Open Ended #5