Question

given that △abc is equilateral, and ad bisects ∠a, show that the side lengths of △adb are in a ratio of 1 : √3 : 2. 1. equilateral triangles are also equiangular, so m∠a = m∠b = m∠c = 60°. 2. by definition of an angle bisector, m∠bad = m∠cad = dropdown with 30°, 45°, 60°

Explanation:

Step1: Split ∠A with bisector

Since $m\angle A = 60^\circ$, the angle bisector divides it into two equal parts.
$m\angle BAD = \frac{60^\circ}{2} = 30^\circ$

Answer:

$30^\circ$