# In Fig. 6.53, ∠1 = ∠ 2 and ∠ 3 = ∠ 4.

(i) Is ∆ADC ≅ ∆ ABC? Why ?

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

**Solution:**

Given, the figure represents two __triangles__ ADC and ABC.

∠1 = ∠2 and ∠3 = ∠4

(i) We have to determine if the triangles ADC and ABC are congruent or not.

Considering triangles ADC and ABC,

Given, ∠1 = ∠2

Common side = AC

Given, ∠3 = ∠4

__ASA congruence__ criterion states that, "if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles will be __congruent__".

By ASA rule, ∆ADC ≅ ∆ABC.

(ii) We have to show that AD = AB and CD = CB

Corresponding parts of congruent triangles or cpct tell us that __corresponding sides__ and __corresponding angles__ of the two triangles which are congruent are equal.

Considering triangles ADC and ABC,

By CPCT,

The corresponding sides are AD;AB and CD;CB

AD = AB

CD = CB

**✦ Try This: **In Fig, is the pair of triangles are congruent?

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 6

**NCERT Exemplar Class 7 Maths Chapter 6 Problem 152**

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

**Summary:**

In Fig. 6.53, ∠1 = ∠ 2 and ∠ 3 = ∠ 4. (i) ∆ADC ≅ ∆ ABC by ASA congruence criterion, (ii) AD = AB and CD = CB by CPCT

**☛ Related Questions:**

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