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
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