Question

ABC is an isosceles triangle with AB = AC. AD is common to triangle ABD and ACD (perpendicular bisector). Then :

$\angle BAD$ = _____

• A. $\angle ACD$
• B. $\angle CAD$
• C. $\angle DCA$
• D. $\angle CDA$

Answer 1

The correct option is B

$\angle CAD$

$\angle CAD$

In isosceles triangle, a perpendicular bisector dividing the triangle will make the triangle look like:

In triangle ABD and ACD,
$\angle BDA$ = $\angle CDA$ = ${90}^{\circ }$

AB = AC [$\because$ ABC is an isosceles triangle]
AD is common

Hence, triangle ABD and ACD are congruent.
$\therefore$ $\angle BAD$ = $\angle CAD$