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Proofs Given: GHIJ is a parallelogram GP ≈ IQ Prove: PX ≈ QX

Proofs Given: GHIJ is a parallelogram GP ≈ IQ Prove: PX ≈ QX-example-1
User Almalki
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statement 1

GHIJ is a parallelogram ----------------> given

N 2

GH=JI -------------> by definition of a parallelogram (opposite sides are congruent)

N3

GP=IQ ------> given

N4

GH=GP+PH ----------> by addition segment postulate

GP=GH-PH

N5

JI=JQ+IQ ---------> by addition segment postulate

IQ=JI-JQ

N6

GH-PH=JI-JQ -------> by substitution

PH=JQ

N7

m by alternate interior angles

N8

m definition of right angle

N9

m definition of right angle

N10

triangle JXQ is congruent to triangle HXP ------> by ASA

N 11

PX≅QX -------> by corresponding sides in congruent triangles

User Lovette
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