Question

If given that the following figure is a parallelogram, which = statements could be used to prove RTS = TRU ? Select all that apply. SSS SAS ASA HL

Answer 1

Explanation:

The question is missing the figure. So, the figure is attached below.Answer:SSSSASASAStep-by-step explanation:Given:Quadrilateral STRU is a parallelogram.A parallelogram is a quadrilateral in which the opposite sides are parallel an equal to each other.Case 1:So, for Δ RTS and Δ TRURS ≅ TU [ Definition of a parallelogram]ST ≅ RU [ Definition of a parallelogram]RT ≅ RT [Common side; Reflexive property]Therefore, the triangles are congruent by SSS postulate.Case 2: ∠4 ≅ ∠8 [ Alternate interior angles are equal]RT ≅ RT [Common side; Reflexive property]∠3 ≅ ∠7 [ Alternate interior angles are equal] Therefore, the triangles are congruent by ASA postulate.Case 3:RS ≅ TU [ Definition of a parallelogram]∠4 ≅ ∠8 [ Alternate interior angles are equal]RT ≅ RT [Common side; Reflexive property]Therefore, the triangles are congruent by SAS postulate. this is his answer.

Answer 2

The question is missing the figure. So, the figure is attached below.

Answer:

SSS

SAS

ASA

Explanation:

Given:

Quadrilateral STRU is a parallelogram.

A parallelogram is a quadrilateral in which the opposite sides are parallel an equal to each other.

Case 1:

So, for Δ RTS and Δ TRU

RS ≅ TU [ Definition of a parallelogram]

ST ≅ RU [ Definition of a parallelogram]

RT ≅ RT [Common side; Reflexive property]

Therefore, the triangles are congruent by SSS postulate.

Case 2:

∠4 ≅ ∠8 [ Alternate interior angles are equal]

RT ≅ RT [Common side; Reflexive property]

∠3 ≅ ∠7 [ Alternate interior angles are equal]

Therefore, the triangles are congruent by ASA postulate.

Case 3:

RS ≅ TU [ Definition of a parallelogram]

∠4 ≅ ∠8 [ Alternate interior angles are equal]

RT ≅ RT [Common side; Reflexive property]

Therefore, the triangles are congruent by SAS postulate.