Question

AC = AD and AB bisects ∠ A as shown in the figure. Which of the following options is/are correct?

• A. BC = BD
• B. ∠CAB = ∠CBA
• C. ∆ ABC ≅ ∆ ABD
• D. All options are correct.

Answer 1

The correct option is D All options are correct.

In triangles ACD and ADB,
AC = AD (given)
AB = AB (common)
∠ CAB = ∠ BAD (given)
Thus, ∆ ABC ≅ ∆ ABD by SAS congruence criterion. Therefere the corresponding parts are equal
$\Rightarrow BC=BD$
$\Rightarrow \angle ACB=\angle ADB$