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?

A. Triangle ACD is similar to triangle ABD.
B. Segment AD is congruent to segment AC.
C. Angle DAC is congruent to angle DAB.
D. Angle CAB is congruent to angle CBA.

Answer 1

A. Triangle ACD is similar to triangle ABD.

Explanation:

Answer 2

C.Angle DAC is congruent to angle DAB

Explanation:

We are given that

AC is congruent to segment AB.

We have to find the statement which is used to prove that angle ABD is congruent to angle ACD.

In triangle ABD and triangle ACD

`AD\cong AD`

Reflexive property of congruency

`AC\cong AB` (given)

`\angle DAB\cong\angle DAC`

`\triangle ABD\cong \triangle ACD`

(SAS Postulate)

`\angle ABD\cong \angle ACD`

(CPCT)

Hence, option C is true.