Question

Write a two-column proof.

Given: Quadrilateral GKJH is a parallelogram
Prove: Triangle GLH is congruent to Triangle JLK

Answer 1

GLH is congruent to JLK as the quadrilateral is a parallelogram,

KJ = GH OR HJ = GK

GL = LJ OR. HL = LK

triangle JKG = GHJ

triangle HGK = KJH

Answer 2

A parallelogram has two pairs of opposite parallel congruent sides.

Given :

Quadrilateral GKJH is a parallelogram,

To prove :

Δ GLH ≅ Δ JLK

Proof :

Statement Reason

1. GH ║ KJ Definition of parallelogram

2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ Alternate interior angle theorem

3. GH ≅ KJ Definition of parallelogram

4. Δ GLH ≅ Δ JLK ASA postulate of congruence

Hence, proved...