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Unit 4 Test – Quadrilaterals and Polygons Honors Geometry 2013-2014 Name: __________________________ Wed. 11/6 or Thu. 11/7 2013 Unit 4 Test Quadrilaterals and Polygons Honors Geometry 2013-2014 Instructions Each question is weighted equally Read instructions to each problem carefully Manage your time to make sure you get something down for every part of every problem Calculators are OK Use the provided “Tools list” as needed Unit 4 Test – Quadrilaterals and Polygons Honors Geometry 2013-2014 1. Multiple Choice Choose all correct options. You might need to select none, some, or all of the options. a. Which of the following statements are TRUE? If a quadrilateral is not a square, then it does not have perpendicular diagonals. If two angles of a trapezoid have been shown to be congruent, then the trapezoid is isosceles. If a quadrilateral has diagonals that are perpendicular but not congruent, then it is a kite. If the diagonals of a quadrilateral are perpendicular and congruent, then it is a square. b. In quadrilateral ABCD, diagonal BD bisects ABC and side AB is NOT congruent to side CD . ABCD could be which of the following? kite parallelogram rectangle trapezoid isosceles trapezoid c. Which of the following could be used as minimum conditions to establish the congruence of two quadrilaterals? SASAS SSSAA SSSSA Two quadrilaterals are parallelograms and they have been shown to have one congruent diagonal. Two quadrilaterals are isosceles trapezoids and they have been shown to have one congruent diagonal. Unit 4 Test – Quadrilaterals and Polygons Honors Geometry 2013-2014 2. Quadrilateral proofs a. Prove the following : If the diagonals of a parallelogram are , then the parallelogram is a rhombus. T S Given: QRST is a and RT SQ Prove: QRST is a rhombus R Statements Reasons Q Unit 4 Test – Quadrilaterals and Polygons Honors Geometry 2013-2014 b. Complete the proof B C Given: AB DC , AB BC and DC BC : Prove: E DEC is isosceles A Statements Reasons D Unit 4 Test – Quadrilaterals and Polygons Honors Geometry 2013-2014 3. Polygons and angles Given a regular octagon ABCDEFG, and two equilateral triangles FGX and DEY. Answer the following questions. No work need be shown, but it can help you get partial credit. You do not need to write or outline proofs of your answers. A a. What is the measure of ABC? B H b. What is the measure of BAC? C G X D F E c. Find ∠𝐷𝑍𝐸 (where point 𝑍 is at the intersection of ⃡𝐸𝐹 and ̅̅̅̅ 𝐷𝑌. d. If you continued adding sides of equal length at equal angles from the vertices X, F, E, and Y, you would construct a gigantic regular polygon below the figure. How many sides would this polygon have? Z Y Unit 4 Test – Quadrilaterals and Polygons Honors Geometry 2013-2014 4. The mid-segment theorem a. Prove the mid-segment theorem: Each mid-segment (segment connecting the midpoints of two sides) of a triangle is parallel to and half the length of the third side. Unit 4 Test – Quadrilaterals and Polygons Honors Geometry 2013-2014 5. The mid-segment parallelogram You were shown the following surprising result during class. Now prove it is true! The figure formed by connecting the midpoints of adjacent sides of any quadrilateral is a parallelogram. Hints – You need to construct a diagonal and you need to use the mid-segment theorem from question 4. You need not have completed the proof of the mid-segment theorem to do this proof. Just use the result. D Z Given: Quadrilateral ABCD with midpoints W, X, W Y, and Z as shown in the diagram. C A Prove: WXYZ is a parallelogram Y X B Statements Reasons