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A day full of math games & activities. Find one near you.

Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer

Solution:

Given, in two triangles an angle of one triangle is equal to an angle of another triangle.

Also, two sides of one triangle are proportional to the two sides of the other triangle.

We have to check if the triangles are similar.

SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Here, two sides of the triangles are equal but these sides do not include the equal angle.

Therefore, the two triangles cannot be similar.

✦ Try This: If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle. Can you say that two triangles will be similar? Why?

Given, in two right triangles one of the acute angles of one triangle is equal to an acute angle of the other triangle.

We have to check if the two triangles can be similar.

Consider two right triangles ABC and PQR

∠A = ∠P = 90°

Given, ∠B = ∠Q (acute angles)

is-it-true-to-say-that-if-in-two-triangles-an-angle-of-one-triangle-is-equal-to-an-angle-of-another-triangle-and-two-sides-of-one-triangle-are-proportional-to-the-two-sides

AAA criterion states that if two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angle will also be equal.

By AAA criterion, the third angle will be equal.

So, ∠C = ∠R

Therefore, the two right triangles are similar

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 12

Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar? Give reasons for your answer

Summary:

Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are not similar as it does not satisfy the SAS criterion

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