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Geometry Quadrilaterals Unit Review Name ______________________________________ Period _______________ Date ________________ G-CO.11 Learning Target: I can prove theorems about parallelograms. 2. Use the figure to answer the questions below. 1. JKLM is a parallelogram. Solve for x and y. (Show all work!) Describe what properties you used. Part A: Give the most specific name for the quadrilateral above. What property identifies it as this shape? Shape? _________________________________ Explanation _____________________________ _______________________________________ _______________________________________ Part B: Solve for x. y = ________ Describe the property used to solve for y: __________________________________________ __________________________________________ x = _______ x = _______ Part C: Find the length of the quadrilateral’s shorter sides. Describe the property used to solve for x: __________________________________________ __________________________________________ Geometry 1 Quadrilaterals Unit Review length = _______ 5/28/14 PUHSD Geometry Curriculum Team 3. Complete the steps of this proof using the below diagram. Given: Parallelogram ABCD 4. Use a compass and straightedge to inscribe regular hexagon in the circle below. Label all vertices of the hexagon. Leave all your construction marks. Prove: C B Statements 1.Parallelogram ABCD 2. AB CD 3. CAD BDA and CDA BAD 4. AD AD 5. CAD BDA 6. C B G-CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Reasons 1. ? 2. ? 3.? 4.? 5.? 6. ? Reason 1 __________________________________________ 5. Use a compass and straightedge to inscribe a square into the circle below. Label all vertices of the square. Leave all construction marks. Reason 2 __________________________________________ Reason 3 __________________________________________ Reason 4 __________________________________________ Reason5 __________________________________________ Reason 6 __________________________________________ Geometry 1 Quadrilaterals Unit Review 5/28/14 PUHSD Geometry Curriculum Team Part B: What are the slopes of each side of the quadrilateral? Show your work. G-GPE.4 Use coordinates to prove simple geometric theorems algebraically. 6. The coordinates of the vertices of a quadrilateral are A (1,5), B (2,2), C (-2,0), and D (-3,3). AB = _______ y 10 BC = _______ CD = _______ –10 10 x AD = _______ –10 Part A: How long is each side of the quadrilateral? Show your work. Part C: What type of quadrilateral is it? Explain your reasoning. Type of quadrilateral _____________________ AB = _______ Explanation: __________________________________________ __________________________________________ BC = _______ __________________________________________ __________________________________________ CD = _______ AD = _______ Geometry 1 Quadrilaterals Unit Review 5/28/14 PUHSD Geometry Curriculum Team