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warm-up after 5.2: Geometry Section 5.3 Show that a Quadrilateral is a Parallelogram 1. Find the values of the variables in the parallelogram. c˚ 18 Learning Target: I can calculate angle measures and segment lengths for parallelograms and determine if a quadrilateral is a parallelogram. [G.CO.11] a = ____ c = ____ b = ____ From Section 5.2 - Properties of Parallelograms Use the diagram of parallelogram XYZW. Complete the statement and give a reason for your answer. If , then opp. sides //. (defn of If , then opp. sides 1. XW ≅ _____ If , then opp. angles 2. ∠XYZ ≅ _____ If , then consec. If , then diagonals bisect each other. s supplementary. If want to prove a quad. is a , use the converses of the properties of a To prove a quadrilateral is a ) . : A. If BOTH pairs of opposite sides are parallel, then it is a B. If BOTH pairs of opposite sides are ≅, then it is a C. If BOTH pairs of opposite angles are ≅, then it is a D. If diagonals bisect each other, then it is a E. If ONE pair of opposite sides are parallel and ≅, then it is a F. If ONE angle is supplementary to 2 (Same - side) consecutive angles, then it is a X W Q 3. XQ ≅ _____ Y Z 4. ∠WYZ ≅ _____ What theorem or definition can you use to show that the quad. is a 1. 2. ? 3. The figure shows part of a stair railing. Explain how you know the support bars MP and NQ are parallel. ft M 2 For what value of x is the quadrilateral a parallelogram? 4. N 3 ft 3 ft f P 2 t Q 5. For what value of x is the quadrilateral a parallelogram? 6.