Question

A triangle can be acute-angled and isosceles.

• A. True
• B. False

Answer 1

The correct option is A True

If any two angles of a triangle are equal but greater than $45°$ then it becomes an acute-angled and isosceles triangle.

e.g.-: In $∆ABC$, $\angle B=50°$ and $\angle C=50°$ are two equal acute angles.

We know, $\angle A+\angle B+\angle C=180°$

$\Rightarrow \angle A+50°+50°=180°$

$\Rightarrow \angle A+100°=180°$

$\Rightarrow \angle A=180°-100°$

$\Rightarrow \angle A=80°$

Since all the angles of $∆ABC$ are less than $90°$ and also sides opposite to the equal angles are equal i.e. $AB=AC$

Therefore,$∆ABC$ is an acute-angled isosceles triangle.

Hence, the given statement is true.