Question

Parallelogram RSTU is shown.

Ilan needs to prove that segment RS ≅ segment TU and segment RU ≅ segment TS. His proof is shown in the table below.

Step Statement
1 RSTU is a parallelogram
2 Side RS || Side TU and Side RU || Side TS
3 ∠RSU≅∠TUS and ∠RUS≅∠TSU
4 Side SU ≅ Side US
5 ΔRSU≅ΔTUS
6 Side RS ≅ Side TU and Side RU ≅ Side TS

Select all reasons that support one or more statements in the proof.

-symmetric property
-opposite sides of a parallelogram are congruent
-alternate interior angles are congruent
-corresponding parts of congruent triangles are congruent
-definition of a parallelogram

Answer 1

• alternate interior angles are congruent
• corresponding parts of congruent triangles are congruent
• definition of a parallelogram

Explanation:

Step Statement ⇒ Reason

1 RSTU is a parallelogram ⇒ Given

2 Side RS || Side TU and Side RU || Side TS ⇒ definition of a parallelogram

3 ∠RSU≅∠TUS and ∠RUS≅∠TSU ⇒ alternate interior angles are congruent

4 Side SU ≅ Side US ⇒ reflexive property

5 ΔRSU≅ΔTUS ⇒ ASA postulate

6 Side RS ≅ Side TU and Side RU ≅ Side TS ⇒ corresponding parts of congruent triangles are congruent