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

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