# In Figure 6.37, if ∆ABE ≅ ∆ACD, show that ∆ADE ~ ∆ABC

**Solution:**

As we know if two triangles are congruent to each other; their corresponding parts are equal.

If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.

This is referred to as SAS (Side - Angle - Side) similarity criterion for two triangles.

In ∆ABE and ∆ACD

AE = AD (DABE ≅ DACD given).......... (1)

AB = AC (DABE ≅ DACD given)......... (2)

Now Consider ∆ADE, ∆ABC

AD/AB = AE/AC from (1) & (2)

and ∠DAE = ∠BAC (Common angle)

⇒ ∆ADE ~ ∆ABC (SAS criterion)

**Video Solution:**

## In Figure 6.37, if ∆ABE ≅ ∆ACD, show that ∆ADE ~ ∆ABC

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.3 Question 6:

In Figure 6.37, if ∆ABE ≅ ∆ACD, show that ∆ADE ~ ∆ABC

In the above figure if ∆ABE ≅ ∆ACD, hence proved that ∆ADE ~ ∆ABC