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?
Answer

Angle CAB is congruent to angle CBA.

Angle DAC is congruent to angle DAB.

Triangle ACD is similar to triangle ABD.

Segment AD is congruent to segment AC.

Answer 1

The right answer for the question that is being asked and shown above is that: "Angle DAC is congruent to angle DAB." The statement that is used to prove that angle ABD is congruent to angle ACD is that Angle DAC is congruent to angle DAB.

Answer 2

Option B is correct.

Angle DAC is congruent to angle DAB

Explanation:

Given: Segment AC is congruent to segment AB.

In ΔABD and ΔACD

`AB \cong AC` [Given]

[Congruent sides have the same length]

AB = AC [Side]

AD = AD [Common side]

`\angle DAC =\angle DAB` [Angle]

Side Angle Side(SAS) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Then by SAS,

`\triangle ABD \cong \triangle ACD`

By CPCT [Corresponding Parts of congruent Triangles are congruent]

then;

`\angle ABD \cong \angle ACD`

therefore, only statement which is used to prove that angle ABD is congruent to angle ACD is: Angle DAC is congruent to DAB