Write a two-column proof for the following

Question

Given: PQRS is a parallelogram. 𝑃𝑇 ≅ 𝑈𝑅

Prove: 𝑄𝑇 ≅ 𝑆𝑈

Answer 1

Statement Reason

1.QT and SU is parallel 1.Given

2.TS and QU is parallel. 2. Congruent

3.TPQ and SUR are congruent 3. SAS Theorem

4.PQRS is a parallelogram 4. CPCTC

Answer 2

Hi,

Given PQRS is a parallelogram and

PT congruent to UR - given

PQ congruent to SR - by definition of parallelogram

angle P is congruent to angle R - opposite angles in a parallelogram are congruent

triangle PQT is congruent to triangle RSU by SAS theorem

QT is congruent to SU by CPCTC