Question

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

Triangle ABC with a segment joining vertex A to point D on side BC. Side AB is congruent to side AC

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

Answer 1

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: Isosceles triangle theorem

Explanation:

In the given picture, there a triangle whose two sides are equal AB=AC.

Therefore it is an isosceles triangle.

Now, the isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.

Therefore by isosceles triangle theorem in ΔABC we have

`\angle{B}=\angle{C}`

Since
`\angle{ACD}=\angle{C}` [Reflexive]

`\angle{ABD}=\angle{B}` [Reflexive]

Therefore,
`\angle{ACD}=\angle{ABD}=`