Drag and drop a statement or reason to each box to complete the proof. given: pq¯¯¯¯¯≅pr¯¯¯¯¯ prove: ∠q≅∠r triangle p q r with segment p q and segment p r each having one tick mark. statement reason pq¯¯¯¯¯≅pr¯¯¯¯¯ given draw pm¯¯¯¯¯¯ so that m is the midpoint of qr¯¯¯¯¯ . two points determine a line. reflexive property of congruence △pqm≅△prm ∠q≅∠r

The proof is explained below.

Step-by-step explanation:

Given a triangle PQR in which PQ=PR.

We have to prove that  ∠Q≅∠R

We prove this by two methods, in a simple way if in triangle two sides are equal then it becomes an isosceles triangle. In triangle PQR sides PQ and PR are equal i.e PQ=PR then PQR becomes an isosceles triangle.

which implies its two base angles are equal gives ∠Q≅∠R

Now, By Congruency postulate,

It is given that draw a line segment PM such that M bisect the line QR i.e M is the mid-point of QR.

In ΔPQM and ΔPRM,

PQ=QR       (Given)

QM=MR       (Given)

PM=PM        (Common)

It gives all the sides equal. Hence, by SSS Postulate, which states that if three sides of two triangles are congruent then these two triangles are congruent.

∴ ΔPQM≅ΔPRM

By CPCT, ∠Q≅∠R