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!

Answer 1

SAS postulate

Explanation:

Triangle ABD equal to triangle CBD.

The postulate that justifies the congruence is - Side angle side.

The Side Angle Side 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 these two triangles are congruent.

Here, AD and CD sides are equal and the two triangles ABD and CBD share a common right angle , so these are congruent or equal as per SAS postulate.

Answer 2

For the answer to the question above, you see that the sides AD and CD are congruent, therefore opposite angles A and C are congruent.
if you want to prove that two triangles are congruent by SAS, you have to show that two corresponding sides are congruent and that the angle between those corresponding sides is congruent also. once you do that, the triangles are proven congruent by SAS