Line AC biscets angle BAD, Line AC bisects angle BCD what postulate proves the triangles congruent

Answer 1

The Angle Bisector Postulate states that if a ray bisects an angle of a triangle, it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

In this case, since line AC bisects both angle BAD and angle BCD, we can determine that:

∠BAD is congruent to ∠DAC (by the definition of angle bisector)
∠DAC is congruent to ∠BCD (by the definition of angle bisector)

Therefore, ∠BAD is congruent to ∠BCD.

This information alone is not sufficient to prove the triangles congruent. However, if we have additional information, such as side lengths or other angle congruences, we can use the Angle-Angle (AA) Postulate or other postulates to prove the triangles congruent.