Question

Angle Q = 90 in triangle PQR. The equilateral triangles APQ, BQR, and CPR are drawn on the sides PQ, QR, and PR, respectively. Prove that APQ + BQR = CPR​​

Answer 1

Step-by-step explanation:

Here triangle PRN is an isosceles triangle with PR = RN. So

angle RNP= angle PNR.

And from triangle PQR, anglePRN= 120 degrees{prq+prn=180}

In triangle PRN, PRN+PNR+RPN=180

120+2PNR=180

2PNR=60

PNR=30

IN TRIANGLE NPQ, ANGLE NPQ=90{NPQ=QPR+NPR=60+30=90}

SO TRIANGLE NPQ IS A RIGHT ANGLED TRIANGLE.

USING PYTHAGORAS THEOREM,

QNsqr=PQsqr+PNsqr

[2PR]sqr=PRsqr+PNsqr {PR=PQ AND QN=2PQ}

4PRsqr-PRsqr=PNsqr

therefore, PN sqr=3

Answer 2

Step-by-step explanation:

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