Question

PLEASE HELP!!!

Ingrid wants to prove that the diagonals of a parallelogram bisect each other, using the figure below.

Which statement and reason should be part of her proof?

A
△QMR≅△SMT by ASA

B
△QMR≅△TMS by ASA

C
△QRS≅△SQT by SSS

D
△QRS≅△RTQ by SSS

Answer 1

Option A.

Explanation:

Given: QRST is a parallelogram and M is the intersection of diagonals.

We know that opposite sides of a parallelogram are parallel and equal.

In △QMR and △SMT,

`\angle MQR=\angle MST` (Alternate interior angles)

`QR=ST` (Definition of parallelogram)

`\angle QRM=\angle STM` (Alternate interior angles)

Two corresponding angles and included sides are congruent.

`\triangle QMR=\triangle SMT` (ASA postulate)

Hence, the correct option is A.