Question

In the figure below, segment AC is congruent to segment AB:

Which statement is used to prove that angle ABD is congruent to angle ACD?
Triangle ACD is similar to triangle ABD.
Triangle ACD is congruent to triangle ABD.
Segment AD is congruent to segment AC.
Segment AD is congruent to segment DC.

Answer 1

Answer:

A would be the right answer.

Step-by-step explanation:

We can prove this using SAS (Side, Angle, Side). This is because segment AD is a side, and we know the angles at point A have to be the same because AD bisects it giving us our angle, and that AC and AB are congruent, yielding our final side. The answer is A. segment AD bisects angle CAB. I just took the exam and I got it right. hope this helps!

Answer 2

Answer:

B.Triangle ACD is congruent to triangle ABD

Step-by-step-explanation:

We are given that AC is congruent to segment AB

We have to prove that angle ABD is congruent to angle ACD

When triangle ACD is congruent to triangle ABD

Then ,Angle ACD is congruent to angle ABD

Angle ADC is congruent to angle ADB

Angle CAD is congruent to angle DAB

Segment CD congruent to segment BD

Because when two triangles are congruent then sides and length of a triangle congruent to its corresponding sides and angles of other triangle .

Therefore,Triangle ACD is congruent to triangle triangle ABD is used to prove that angle ABD is congruent to angle ACD.

Hence, option B is true.