4.Prove that the ratios of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
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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Answer:
no problem i'll tell it later on
Step-by-step explanation:
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