Question

Are the angles opposite to the equal sides of an isosceles triangle are equal to each other?

• A. Yes
• B. No

Answer 1

The correct option is A Yes

Suppose, an isosceles $△ABC$ such that $AB=AC$
$\underset{–}{\text{To prove:}}$
angles opposite to equal sides are equal i.e $\angle C=\angle B$
$\underset{–}{Proof:}$
Take a point $D$ on $BC$ such that $DB=DC$ and join $AD$
Now, In $△ADB\text{and}△ADC,$
$AB=AC$ [Given]
$DB=DC$ [By construction]
$AD=AD$ [Common side]
$\therefore \text{By S.S.S congruency}△ADB\cong △ADC$
Hence, $\angle C=\angle B$
[Corresponding parts of congruent triangles are equal]