Question

show that triangle PQR is an isosceles triangle in which PQ= PR​

Answer 1

Answer:

Inorder to prove triangle PQR is an isosceles triangle, we must prove that triangle PZQ = triangle PZR

In Triangle PZQ and PZR,

QZ = ZR ( Given in the question PZ Bisects QR)

PZ = PZ ( Common)

Angle PZR = Angle PZQ ( Both are 90° linear pair)

Hence,

Triangle PZQ is congruent to Triangle PZR due to RHS Congruence rule.

The sides of the triangle will be equal and it is a isosceles triangle.

Answer 2

Answer:

Δ PQR is an isosceles triangle

Step-by-step explanation :

In Δ PQZ and Δ PRZ

• PZ = PZ ( common )
• ∠PZQ = ∠PZR
• QZ = RZ ( given - PZ is the perpendicular bisector )

By SAS congruency rule ΔPQZ congruent to  ΔPRZ

By CPCT PQ = PR

∴ Δ PQR is an isosceles triangle

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