Question

Prove that Angles opposite to equal sides of an isosceles triangle are equal​

Answer 1

Answer:

HERE IS UR ANSWER:-

Step-by-step explanation:

Let there be a triangle abc

Draw ap bisects angle a

Since ap is a bisector

There are 2 triangles formed

Let's prove that those 2 triangles are congruent

Angle bap =cap (ap bisects angle a)

Ap=ap (common side)

Ab =ac (given)

Therefore triangle abp is congruent to triangle apc

Angle abc =acp (corresponding parts of congruent triangles (cpct)

Therefore angles opposite to equal sides of an isosceles triangle are equal

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Answer 2

Answer:

ABC is a given triangle with, AB=AC.

To prove: Angle opposite to AB= Angle

opposite to AC (i.e) ∠C=∠B

Construction: Draw AD perpendicular to BC

∴∠ADB=∠ADC=90

o

Proof:

Consider △ABD and △ACD

AD is common

AB=AC

∴∠ADB=∠ADC=90

o

Hence ∠ABD=∠ACD

∠ABC=∠ACB

B=∠C. Hence the proof