Question

Triangle ABD equal to triangle CBD. Name the theorem or postulate that justifies the congruence.
(There is a diagram)
When you get your answer could you please tell me how you got it? Thank you!
I think it is SAS but I could be wrong.

Answer 1

Since the sides AD and CD are congruent, opposite angles A and C are congruent. You see that?

Answer 2

@mathstudent55 yes I do

Answer 3

Ok, let's go back to your answer, SAS. To prove triangles congruent by SAS, you have to have two sides and the included angle. You don't have that.

Answer 4

@mathstudent55 so is it ASA?

Answer 5

Side BD is congruent to itself.
Angle ABD is congruent to angle CBD
Side AD is congruent to side CD
The problem is those two sides are not the sides that include the congruent angles.
So it's not SAS

Answer 6

For ASA, you need two angles and the side between them. You don't have that either.

Answer 7

Now go back to what I wrote above.
Since the sides AD and CD are congruent, opposite
angles A and C are congruent. (1)
Next you have angles ABD and CBD are congruent. (2)
Finally you have sides AD and CD are congruent, (3)
so you have in order,
(1) Angle-(2) Angle-(3) Side.
The triangles are congruent by AAS

Answer 8

@mathstudent55 AH! I get it now! Thank you so much, best answer is yours!

Answer 9

You're welcome.