Question

State and prove theorem 7.2​

Answer 1

Answer:

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Answer 2

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Step-by-step explanation:

Theorem 7.2 : Angles opposite to equal sides of an isosceles triangle are equal. This result can be proved in many ways....

Proof : We are given an isosceles triangle ABC in which AB = AC. We need to prove that ∠ B = ∠ C.

Let us draw the bisector of ∠ A and let D be

the point of intersection of this bisector of

∠ A and BC (see Fig. 7.25 in NCERT).

In ∆ BAD and ∆ CAD,

AB = AC (Given)

∠ BAD = ∠ CAD (By construction)

AD = AD (Common)

So, ∆ BAD ≅ ∆ CAD (By SAS rule)

So, ∠ ABD = ∠ ACD, since they are corresponding angles of congruent triangles.

So, ∠ B = ∠ C