Question

Fill in the missing statements and reasons in the proof.
Given: PQRS is a parallelogram.
Prove: PR and QS bisect each other at T.

Answer 1

1. Given in the problem
3. Alternate interior angles are congruent
5. ASA congruence postulate
6. Coresponding sides of congruante triangles are congruante
7. PR and QS bisect each other at T

Answer 2

Answer:

We have to complete the proof.

PQRS is a parallelogram          1. Given

2. $\overline{PQ}\:is\:parallel\:to\:\overline{RS}$    Definition of a parallelogram

m∠1 ≅ m∠3                  4. Alternate interior angles are equal or

m∠2 ≅ m∠4                       congruent.

$\overline{PQ}\:\cong\:\overline{RS}$      Opposite sides of a parallelogram are congruent

ΔPQT ≅ ΔRST     5. Triangle are congruent by Angle-Side-

                                 Angle congruent rule

$\overline{PT}\:\cong\:\overline{RT}$   6. Corresponding parts of Congruent triangles

$\overline{QT}\:\cong\:\overline{ST}$

7. PR and QS bisect each other at T          Definition of a bisector