Question

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Angles opposite to equal sides of a triangle are equal

Sides opposite to equal angles of a triangle are equal​

Answer 1

Answer:

q1

Given :-

A Triangle ABC

with AB = AC

To prove :-

Angle B = Angle C

Construction:-

Draw the bisector AD of angle A meeting BC at D

Proff :-

In triangles ABD and ACD

AB = AC ( Given)

Angle 1 = Angle 2 ( As AD bisects Angle A)

AD = AD ( Common )

Therefore by SAS Congrency

Triangle ABD = Triangle ACD

So

Angle B = Angle C ( C.P.C.T)

Hence proffed

Therefore Angles opposite to equal sides of a triangle are equal

q2

Given :-

A Triangle ABC

Angle B = Angle C

To prove :-

AB= AC

Construction :-

Draw bisectors of Angle A meeting BC at D

Proff :-

In triangle ABD and ACD

Angle B = Angle C ( given )

Angle 1 = Angle 2 ( as AD bisects Angle A )

AD = AD (Common )

Therefore ,

By AAS Congrency

Triangle ABD is congrent to Triangle ACD

There fore

AB = AC ( C.P.C.T)

Hence proffed

Therefore Sides opposite to equal angles of a triangle are equal

Note :-

Figure in attachment