4.Prove that the ratios of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
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Step-by-step explanation:
for proving theorem we use concept of area of triangle and property of Similarities of triangle
Attachments:
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Question
Prove that the ratios of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
Answer
Given :-
- We are given two triangles ABC and PQR such that ΔABC∼ΔPQR.
To prove :-
Construction:-
- Draw altitudes AM & PM of the triangles.
Now ,
So,
Now , In ΔABM & ΔPQN,
∠B = ∠Q. ......( As ΔABC∼ΔPQR)
∠M = ∠N. ....( Each is of 90°)
So,
ΔABM∼ΔPQN. .....................(AA similarity criterion)
Therefore,
Also,
ΔABC∼ΔPQR. .......................(Given)
So,
Therefore,
Now, using( 3), we get
Attachments:
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