Question

32
Prove that the angle opposite to the equal sides of an equilateral
triangle are equal​

Answer 1

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 proved