Question

In a triangle $ABC$, $\angle A={40}^o$ and $AB=AC$, then $ABC$ is ............ triangle.

• A. right angled
• B. equilateral
• C. isosceles
• D. scalene

Answer 1

Answer: (C)

isosceles

Given: in triangle $ABC,AB=AC$

Draw perpendicular from point $A$ on line $BC$ which cut at point $D$

Consider, triangles $ADB$ and $ADC$

$AB=AC$ (Given)

$\angle ADB=\angle ADC={90}^o$ .... [Since $AD$ perpendicular on $BC$]

$AD=AD$ [Common side]

$\therefore △ADB\cong △ADC$ ..... [By SAS congruence rule]

$\therefore \angle B=\angle C$

$\therefore$ In $△ABC,\angle B=\angle C$

Thus, $△ABC$ is an isosceles triangle.

Hence, option C is correct.