Q. 1525.0( 3 Votes )

# In Fig. 6.53, ∠1 = ∠2 and ∠3 = ∠4.

(i) Is ∆ADC ≅ ∆ABC? Why?

(ii) Show that AD = AB and CD = CB.

Answer :

Given: ∠1 = ∠2 and ∠3 = ∠4

**Formula Used/Theory:-**

→ when 2 angles and side between both the angles are equal in both the triangles then triangles are congruent by ASA congruence criterion

In ∆ADC and ∆ABC

∠1 = ∠2 (Given)

∠3 = ∠4 (Given)

AC = AC (common)

∆ADC ≅ ∆ABC

⇒ Hence; both triangles are congruent by ASA congruence

If ∆ADC ≅ ∆ABC then;

If triangles are congruent then all 3 sides of triangle are equal to all 3 sides of other triangle

AC = AC

⇒ AD = AB

⇒ CD = CB

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Complete the congruence statement:

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