Question

PLEASE HELP ME ASAP!!! I REALLY NEED HELP :(

Answer 1

See below

Explanation:

Given

• R is the midpoint of SQ and PT

To prove

• ΔPQR ≅ ΔTSR

Solution

R is the midpoint of SQ

• SR = 1/2SQ and RQ = 1/2SQ ⇒ SR ≅ RQ

R is the midpoint of PT

• PR = 1/2PT and RT = 1/2PT ⇒ PR ≅ RT

SQ and PT intersect at point R ⇒

• ∠PRQ ≅ ∠TRS as vertical angles

Triangles PQR and TSR have two sides and the included angle congruent, therefore:

• ΔPQR ≅ ΔTSR,

as per SAS congruence postulate

• If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent