Question

If in $\Delta ABC,\angle A={60}^{\circ }$ and $AB=AC$ , then $\Delta$ $ABC$ is

• A. an isosceles $\Delta$
• B. a right angled $\Delta$
• C. a isosceles right angled $\Delta$
• D. an equilateral $\Delta$

Answer 1

The correct option is D an equilateral $\Delta$

In $△ABC$, $AB=AC$

$\angle B=\angle C$ [Opposite angle are equal]

Now,

Sum of all angles of a triangle is ${180}^0$

Thus,

$\angle A+\angle B+\angle C={180}^0$

$=>60+\angle B+\angle +B=180$

$=>2\angle B={120}^0$

$=>\angle B={60}^0$

$=>\angle C={60}^0$

Thus, all angles are ${60}^0$

Thus, $△ABC$ is a equilateral triangle