Question

Segment AC is the angle bisector of The figure is not to scale.

Which of the following additional statements would allow us to prove that

Answer 1

What does this problem ask for:

--> which statement is sufficient to prove that:

∠ADB ≅ ∠ABD

Let's separate this image into two triangles: ΔADC and ΔABC

--> prove that these triangles are congruent

--> thus proving that: ∠ADB ≅ ∠ABD

Let's consider what evidence we have:

• AC is angle bisector of ∠BAD

--> thus: ∠ADC = ∠ABC

• AC = AC

The minimum information that we have:

--> prove that one pair of sides on both triangles are congruent

--> based on the SSA Triangle Formula

--> Two triangles that have two sides and one angle that are

equal, are therefore congruent

Based on the choices given:

--> if DA = BA or DA is congruent to BA

--> then ΔADC = ΔABC

Thus:

--> ∠ADC = ∠ABC

Answer: DA is congruent to BA