ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (Fig. 6.48).
(a) State three pairs of equal parts in the triangles ABD and ACD.
(b) Is ∆ABD ≅ ∆ACD. If so why?

Solution:

Given, ABC is an isosceles triangle with AB = AC.

D is the mid-point of base BC.

We have to state the three pairs of equal parts in the triangles ABD and ACD and determine if ∆ABD ≅ ∆ACD.

Considering triangle ADB and ADC,

Given, AB = AC

Since D is the midpoint of BC,

BD = CD

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, ∆ABD ≅ ∆ACD

✦ Try This: Without drawing the triangles write all six pairs of equal measures in each of the following pairs of congruent triangles ∆TUV ≅ ∆DEF

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 144

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (Fig. 6.48). (a) State three pairs of equal parts in the triangles ABD and ACD. (b) Is ∆ABD ≅ ∆ACD. If so why?

Summary:

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (Fig. 6.48). The three pairs of equal parts in the triangles ABD and ACD are AB = AC; BD = CD and AD. By SSS congruence criterion, ∆ABD ≅ ∆ACD.

☛ Related Questions:

• In Fig. 6.49, it is given that LM = ON and NL = MO. (a) State the three pairs of equal parts in the . . . .
• Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = . . . .
• If ∆PQR and ∆SQR are both isosceles triangle on a common base QR such that P and S lie on the same s . . . .