# Observe Fig. 6.54 and state the three pairs of equal parts in triangles ABC and DBC.

(i) Is ∆ABC ≅ ∆DCB? Why?

(ii) Is AB = DC? Why?

(iii) Is AC = DB? Why?

**Solution:**

Given, the figure represents two triangles ABC and DCB.

We have to state the three pairs of equal parts in triangles ABC and DBC and determine if the triangles are __congruent__ or not.

Considering triangles ABC and DCB,

∠ABC = ∠DCB = 70°

Common side = BC

∠ACB = ∠DBC = 30°

__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, ∆ABC ≅ ∆DCB.

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 ABC and DCB,

By CPCT,

AB = DC

AC = DB

**✦ 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 153**

## Observe Fig. 6.54 and state the three pairs of equal parts in triangles ABC and DBC. (i) Is ∆ABC ≅ ∆DCB? Why? (ii) Is AB = DC? Why? (iii) Is AC = DB? Why?

**Summary:**

Observe Fig. 6.54 and state the three pairs of equal parts in triangles ABC and DBC. (i) ∆ABC ≅ ∆DCB by ASA congruence criterion, (ii) AB = DC by CPCT, (iii) AC = DB by CPCT

**☛ Related Questions:**

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