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In Fig. 6.5, if ∠D = ∠C, then is it true that △ADE ~ △ACB? Why

Solution:

Given, in the triangles ADE and ACB ∠D = ∠C

We have to determine if the triangles ADE and ACB are similar.

From the figure,

It is clear that A is the common angle.

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 must be equal.

∠B = ∠E

So, △ADE ~ △ACB

Therefore, the triangles ADE and ACB are similar.

✦ Try This: In the given figure, ∠B = ∠C = 55º and ∠D = 25º. Then ∠BAC is equal to

in-fig-6-5-if-d-c-then-is-it-true-that-ade-acb-why

Given, ∠B = ∠C = 55º

Also, ∠D = 25º

We have to find the value of ∠CAD.

As ∠B = ∠C, the sides AB and AC will be equal.

So, the triangle ABC is isosceles.

We know that the sum of all the three interior angles of a triangle will always be equal to 180º

So, ∠B + ∠C + ∠BAC = 180º

55º + 55º + ∠BAC = 180º

110º + ∠BAC = 180º

∠BAC = 180º - 110º

Therefore, ∠BAC = 70º

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

NCERT Exemplar Class 10 Maths Exercise 6.2 Problem 11

In Fig. 6.5, if ∠D = ∠C, then is it true that △ADE ~ △ACB? Why

Summary:

In Fig. 6.5, if ∠D = ∠C, then △ADE ~ △ACB is true as it satisfies AAA criterion

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