Question

Prove that when two triangles are similar, the ratio of areas of those triangles is equal
to the ratio of the squares of their corresponding sides. (Areas of Similar Triangle
(Proof))

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Answer 1

Answer:

Given:△ABC∼△PQR

To prove:ar(△PQR)ar(△ABC)=(PQAB)2=(QRBC)2=(PRAC)2

Construction:Draw AM⊥BC and PN⊥QR

Proof:area(△ABC)=21×base×height=21×BC×AM         ........(1)

area(△PQR)=21×base×height=21×QR×PN         ........(2)

Dividing (1) by (2) we get

ar(△PQR)ar(△ABC)=21×QR×PN21×BC×AM

=QR