5.02 Parallelogram Proofs.pdf - Course Geometry Unit...

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Unformatted text preview: Course: Geometry Unit: Quadrilaterals and Polygons Section: Parallelograms Assignment: Parallelogram Proofs Points: 50 1. Given parallelogram WXYZ, complete each statement and state the property or definition that justifies your answer. [1 point for each blank and 2 points for justification. 20 points total.] W X C Z XY a. WZ || _______ Y Justification: If a quadrilateral is a parallelogram, then its opposite sides are parallel. XC b. ZC ≅ _______ WC and YC ≅ _______ Justification: <WZY c. ∠WXY ≅ _______ Justification: d. WC = 1 WY _______ 2 and XC = 1 XZ _______ 2 Justification: WXY are supplementary. e. ∠XYZ and _______ Justification: <ZCY f. ∠WCX ≅ _______ Justification: If a quadrilateral is a parallelogram, then the diagonals bisect each other. If a quadrilateral is a parallelogram, then the opposite angles are congruent. If two diagonals bisect each other, then 0.5 of the diagonal is the midpoint. If a quadrilateral is a parallelogram, then the consecutive angles aresupplementary If two diagonals bisect each others, then the vertical angles are congruent. 2. Write a two-column proof. Given: ABDE and CDFG are parallelograms Prove: ∠G ≅ ∠A [15 points for statements, 15 points for reasons. 30 points total.] E D C B F G A Statements: Reasons -ABDE and CDFG are parallelograms: Given -Angle D is congruent to angle D: reflexive property of equality -Angle G and Angle D are opposite angles: Definition of opposite angles -Angle G is congruent to angle D: Opposite angles of a parallelogram are congruent -Angle D is opposite to angle A: Definition of opposite angles -Angle D is congruent to angle A: Opposite angles of a parallelogram are congruent -Angle G is congruent to angle A: Transitive property of equality ...
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