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Q.

Is the following statement true or false?

The given triangles are similar.

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a

True

b

False

answer is A.

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Detailed Solution

AAA (angle-angle-angle) similarity test theorem is true when two triangles have their corresponding angles equal only if their corresponding sides are proportional.
Given are the two triangles.
Question Image

Question Image

The given triangles are similar as their corresponding angles are equal and the corresponding sides are also proportional.
From the given figures we have,

∠ B A C = ∠ Q P R = 60 ° ∠ A B C = ∠ P Q R = 80 ° ∠ A C B = ∠ P R Q = 40 °

By AAA similarity theorem we get

Δ ABC ~ Δ PQR

.
Therefore by AAA similarity criterion

Δ ABC ~ Δ PQR

, which is true.
Therefore the correct option is 1.

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Is the following statement true or false?The given triangles are similar.