Question

R
AABC is an equilateral triangle. P, Q, R are points on sides AB, BC and
CA respectively such that AP = BQ = CR. Prove that PQ = QR = RP.​

Answer 1

Explanation:

Given: ABC is an equilateral triangle. P, Q, R are points on AB, BC, CA respectively, such that

AP=BQ=CR

We know, AB=BC=CA

AP=BQ=CR

AB−AP=BC−BQ=CA−CR

BP=CQ=AR (I)

Now, In △APR and △PBQ

∠A=∠B=60

∘

AP=BQ (Given)

BP=AR (From I)

Thus, △APR≅△BQP (SAS rule)

Hence, PQ=PR (By cpct)...(II)

Similarly, △APR≅△CRQ

hence, PR=QR ..(III)

thus, from II and III

PQ=QR=PR

∴△PQR is an equilateral triangle.

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Answer 2

Explanation:

I have attached the answer of question

AABC is an equilateral triangle. P, Q, R are points on sides AB, BC and

CA respectively such that AP = BQ = CR. Prove that PQ = QR = RP.