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If D is the midpoint of the side BC in ∆ABC where AB = AC, then ∠ADC is
(a) 60°
(b) 45°
(c) 120°
(d) 90°

Solution:

Given, ABC is a triangle with AB = AC

D is the midpoint of the side BC.

We have to find the measure of ∠ADC.

If D is the midpoint of the side BC in ∆ABC where AB = AC, then ∠ADC is: (a) 60°, (b) 45°, (c) 120°, (d) 90°

Considering triangle ADB and ADC,

Since D is the midpoint,

BD = CD

Given, AB = AC

Also, common side = AD

Side-Side-Side congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.

By SSS rule, ΔABD ≅ ΔACD

Corresponding parts of congruent triangles or cpct tell us that corresponding sides and corresponding angles of the two triangles which are congruent are equal.

By CPCT rule,

∠ADB = ∠ADC --------------------- (1)

We know that the sum of a linear pair of angles is equal to 180 degrees.

So, ∠ADB + ∠ADC = 180°

From (1),

∠ADC + ∠ADC = 180°

2∠ADC = 180°

∠ADC = 180°/2

Therefore, ∠ADC = 90°

✦ Try This: The sides of a triangle have lengths (in cm) 15, 12 and x, where x is a whole number. The minimum value that x can take is

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 44