Question

Isosceles ABC, with right angle at B, has a point D on AC such that BD is parallel to AC. What is the relationship between triangle AABD and triangle ACBD? Explain.

Answer 1

Triangle AABD is congruent to triangle ACBD.

Step-by-step explanation:

Triangle AABD is congruent to triangle ACBD.

Since triangle ABC is an isosceles triangle with a right angle at B, the base angles A and C are congruent. Therefore, angle ABD is congruent to angle CBD. Since BD is parallel to AC, angle BDA is a right angle.

By the Angle-Angle Similarity Postulate, triangles AABD and ACBD are congruent.