in figure 11.31 PQ=PR and SQ=SR prove that angle PQS= angle PRS
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The prove is given below—
Step-by-step explanation:
In ∆PQR,
PQ=PR
So, ∆PQR is an isoceles triangle.
Which means, ∠PQR=∠PRQ
After that,
In ∆SQR,
SQ=SR
So, ∆SQR is an isoceles triangle.
Which means, ∠SQR=∠SRQ
Let ∠PQR be x so ∠PRQ will be also x
And let ∠SQR be y so ∠SRQ will be also y
∠PQS=∠PQR–∠SQR=x–y
So, ∠PQS=x–y
∠PRS=∠PRQ–∠SRQ=x–y
So, ∠PRS=x–y
Therefore, x–y=x–y
Hence, ∠PQS=∠PRS. (proved)
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