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If one pair of opposite sides of a quadrilateral are BOTH congruent and parallel, then the quadrilateral is a parallelogram! Summary: Proving Quadrilaterals are Parallelograms. ü Show that both pairs of opposite _______ are _________________.
Draw a picture of each quadrilateral, to determine if it is a parallelogram by one of the following reasons. Be able to explain your selection. a) Opposite sides congruent. b) Opposite angles congruent. c) Diagonals bisect each other. d) One pair of opposite sides is both parallel and congruent. e) Both pairs of opposite sides are parallel.
Draw a picture of each quadrilateral, to determine if it is a parallelogram by one of the following reasons. Be able to explain your selection. a) b) c) d) 21) 22) 23) 24) 25) Opposite sides congruent. Opposite angles congruent. Diagonals bisect each other.
Proofs with Parallelograms Practice Questions 1 through 4 refer to the following: Given: Quadrilateral ABCD below 1) If AD H BC and AD C BC , determine whether quadrilateral ABCD is a parallelogram. [ Explain your answer.] 2) If AD C DC and AB C BC , determine whether quadrilateral ABCD is a parallelogram. [ Explain your answer.]
Given a parallelogram, you can use the Parallelogram Opposite Sides Theorem (Theorem 7.3) and the Parallelogram Opposite Angles Theorem (Theorem 7.4) to prove statements about the sides and angles of the parallelogram.
Geometry Worksheet Quadrilaterals Section: Name: Mr. Lin 5 32. Congruent & Parallel Opposite Sides If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram Prove: Given: If € AB || € CD, and € AB ≅ € CD
6.3 Proving Quadrilaterals are Parallelograms 341 USING COORDINATE GEOMETRY When a figure is in the coordinate plane, you can use the Distance Formula to prove that sides are congruent and you can use the slope formula to prove that sides are parallel. Using Properties of Parallelograms Show that A(2, º1), B(1, 3), C(6, 5), and D(7, 1)