Question

Which statement is used to prove that angle ABD is congruent to angle ACD?

Answer 1

Choices:
Segment AD bisects angle CAB.
Triangle ACD is similar to triangle ABD.
Segment AD is congruent to segment AC.
Angle CAB is congruent to angle CBA.

The statement that is used to prove that angle ABD is congruent to angle ACD is SEGMENT AD IS CONGRUENT TO SEGMENT AC.

The small line that marked both segments means that both segments have the same measure.

Answer 2

The required Statement is In a triangle angles opposite to equal sides are equal that is ∠ACD ≅ ∠ABD

Explanation:

Given: AC = AB

We have to given a statement which prove that ∠ACD congruent to ∠ABD.

Consider, ΔABC

AC = AB (given)

We use the result which says that

In a triangle angles opposite to equal sides are equal.

⇒ ∠ACB = ∠ABC or ∠ACD ≅ ∠ABD

Therefore, The required Statement is In a triangle angles opposite to equal sides are equal that is ∠ACD ≅ ∠ABD