Question

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❤✌✌Class 10th question❤✌✌


Prove that the ratio of the areas of two similar triangles is equal to the square of
the ratio of their corresponding medians.

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Answer 1

Given:

• ∆ABC and ∆PQR are similar
• AB/BC = PQ/QR = AC/PR
• angle A = angle P
• angle B = angle Q
• angle C = angle R

Let AD and PM be the medians of ∆ABC and ∆PQR respectively.

TO PROVE: AD²/PM² = ar( ∆ABC ) / ar( ∆PQR )

PROOF

In ∆ABD and ∆PQM,

angle B = angle Q ( given )

AB/PQ = BC/QR

= 2BD/2QM [ Since Median bisects the side ]

AB/PQ = BD/QM

•°• By SAS criteria ,

∆ABD ~ ∆PQM

•°• AB/PQ = AD/PM --(1) ( C.P.S.T )

We know Ratio of two similar triangles is equal to the ratio of their corresponding sides.

•°• ar(∆ABC) \ ar(∆PQR) = AB² / PQ²

ar(∆ABC) \ ar(∆PQR) = AD² / PM² [ Since AB/PQ = AD/PM from eq.(1) ]

Hence, Proved.

Answer 2

Answer:

Refer the attachment

Explaination is done in attachment ✌️✌️