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

i have Angle DAC is congruent to angle DAB. as my answer is that correct?

Answer 2

I hope you are learning the work here

Answer 3

yep =) do you know if the answer i chose is the correct answer?

Answer 4

yup I think so

Answer 5

ok cool thank-you =)

Answer 6

yw

Answer 7

i don't think there is enough information to justify. If D is the midpoint of BC, then the answer you chose is correct.

Answer 8

yeahh i thought about that to but if we are told that the two outer sides are congruent and they share a side then wouldn't the third side have to be the same for both to?

Answer 9

hmm it's provided that AD is perpendicular to BC. okay lets say you move the point D slightly towards C, then you will see that both AC and AB are congruent, they do share the same side AD, but angle DAC is not the same as angle DAB in fact angle DAB>angleDAC.

Answer 10

do in that case it would be similar?

Answer 11

nope. the 2 triangles DAC and DAB have to have at last 2 equal angles to be considered similar triangles. If D is not the midpoint, the only angle which are equal would be angle C and B. so i think that D is the midpoint for this question.

Answer 12

mmkkk. thank-you

Answer 13

you're welcome. :)