UMTYMP Geometry Fall 2015 Quiz.pdf

UMTYMP Geometry Name (Print): Fall 2015 Quiz 1 10/8/2015 Time Limit: 60 Minutes This exam contains 6 pages (including this cover page) Page Points Score and 9 problems. Check to see if any pages are missing....

UMTYMP Geometry Name (Print): Fall 2015 Quiz 1 10/8/2015 Time Limit: 60 Minutes This exam contains 6 pages (including this cover page) Page Points Score and 9 problems. Check to see if any pages are missing. 2 8 You may not use your books, notes, or any calculator 3 13 on this exam. 4 12 You are required to show your work on each problem on 5 11 this exam. The following rules apply: 6 11 Total: 55 Organize your work, in a reasonably neat and coherent way, in the space provided. Work scat- tered all over the page without a clear ordering will receive very little credit. Mysterious or unsupported answers will not receive full credit. A correct answer, unsup- ported by calculations, explanation, or algebraic work will receive no credit; an incorrect answer supported by substantially correct calculations and explanations might still receive partial credit. If you need more space, use the back of the pages; clearly indicate when you have done this. Do not write in the table to the right. UMTYMP Geometry Quiz 1 - Page 2 of 6 10/8/2015 1. (8 points) Use a compass and straightedge to do the following constructions using the line and segments below. (a) (4 points) Mark a point Y on ` such that XY = M N − AB. (b) (4 points) Construct the perpendicular bisector of M N ` X M N B A UMTYMP Geometry Quiz 1 - Page 3 of 6 10/8/2015 2. (8 points) Find the measure of the indicated angles using the figure below. Note that ` k m and rays o and p bisect angles. (2 Points each) m h p a b 20◦ ` c d e g 40◦ f o n (a) ∠a = (c) ∠c = (e) ∠e = (g) ∠g = (b) ∠b = (d) ∠d = (f) ∠f = (h) ∠h = 3. (5 points) Given that AB k EF , find x. UMTYMP Geometry Quiz 1 - Page 4 of 6 10/8/2015 4. (6 points) Given: Figure with AB = AD, CB = CD, E is the intersection of AC and BD. Prove: 4AEB ∼ = 4AED 5. (6 points) In the figure below, let a = [ABC]. Find the areas of the other triangles in terms of a. Show your work. You may assume the grid is square and to scale so that, for example, AC = CD. (3 Points each) (a) [AEC] = (b) [ABD] = (c) [AF D] = UMTYMP Geometry Quiz 1 - Page 5 of 6 10/8/2015. Given: Figure with ∠AEC ∼ = ∠BF D, AB = CD and EC k F D 6. (6 points) Prove: 4AEC ∼ = 4BF D E F A B C D 7. Suppose a rectangle has width x and height y. (a) (3 points) If we double the width of the rectangle, what must we do to the height to keep the area unchanged? Explain. (b) (2 points) Find the perimeter of this new rectangle. UMTYMP Geometry Quiz 1 - Page 6 of 6 10/8/2015 8. (6 points) Given: AB = AC in 4ABC. Prove: ∠ABC = ∠ACB Note: You cannot simply state that the triangle is isosceles; you are being asked to prove this fact about isosceles triangles. 9. (5 points) Draw a diagram to demonstrate why there is no SSA congruence theorem. Make sure to explain why your diagram show this.