Given: quadrilateral TALK is a parallelogram.

Prove: TA congruent LK and AL congruent KT

Proved by ASA congruence rule.

Step-by-step explanation:

Given the parallelogram TALK. We have to prove that TA is congruent to LK and AL is congruent to KT.

∵ TALK is a parallelogram,

AL is parallel to segment TK and TA is parallel to KL and Line TL is a transversal.

⇒ ∠1 ≅ ∠ 4 and ∠2 ≅ ∠ 3

In ΔTLK and ΔTLA

∠1 = ∠ 4 (∵Alternate angles)

∠2 = ∠ 3 (∵Alternate angles)

TL=TL (∵Common)

By ASA rule, ΔTLK ≅ ΔTLA

∴ By CPCT (Corresponding Parts of Congruent Triangles), TA ≅ LK and segment AL ≅ KT

Hence Proved