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

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

Respuesta :

s1m1
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:

We have to complete the proof.

PQRS is a parallelogram          1. Given

2. [tex]\overline{PQ}\:is\:parallel\:to\:\overline{RS}[/tex]    Definition of a parallelogram

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

m∠2 ≅ m∠4                       congruent.

[tex]\overline{PQ}\:\cong\:\overline{RS}[/tex]      Opposite sides of a parallelogram are congruent

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

                                 Angle congruent rule

[tex]\overline{PT}\:\cong\:\overline{RT}[/tex]   6. Corresponding parts of Congruent triangles

[tex]\overline{QT}\:\cong\:\overline{ST}[/tex]

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

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