In Fig. 6.53, ∠ 1 = ∠ 2 and ∠ 3 = ∠ 4. (i) Is ∆ADC ≅ ∆ABC? Why? (ii) Show that AD = AB and CD = CB.

Question

Philoid · Accepted 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