Question

In the given figure, triangles PQC and PRC are such that QC = PR and PQ = CR. Prove that ∠PCQ = ∠CPR.

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Answer 1

in triangle PQC and triangle PRC,
Given - QC= PR
PQ=CR
To prove:- angle PCQ= angle CPR


Proof:- In triangle PQCand triangle PRC:-

QC=PR [GIVEN]
PQ=CR [GIVEN]
andPC=PC [COMMON]

by SAS similarly criterion, triangle PQC is congruent to triangle PRC.


therefore by C.P.C.T


angle PCQ =angle CPR
prooved.

Answer 2

Given:

In the given figure, triangles PQC and PRC are such that QC = PR and

PQ = CR.

To Find:

Prove that ∠PCQ = ∠CPR

Solution:

Here, we have

QC = PR       [ GIVEN ]

PQ = CR       [GIVEN]

PC = PC       [COMMON]

by SAS similarly criterion,

ΔPQC ≅ ΔPRC.

Therefore by C.P.C.T,

∠PCQ = ∠CPR

Hence, ∠PCQ = ∠CPR.