1.

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

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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


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