Respuesta :

mhanifa

Answer:

See below

Step-by-step 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