The question is missing the figure. So, the figure is attached below.
Answer:
SSS
SAS
ASA
Step-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 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.
