Final answer:
Triangles BDA and BDC are similar by AA Similarity because they are both right triangles that share angle B, and BD is perpendicular to AC, creating the two right angles needed.
Step-by-step explanation:
The question asks for a proof to show that triangles BDA and BDC are similar. Given that BC = BA and BD is perpendicular to AC, we can use the AA Similarity postulate to prove the similarity of the triangles.
Since BD is perpendicular to AC, it creates two right angles; therefore, Triangle BDA and Triangle BDC are both right triangles. In right triangles, the right angle itself is one of the two angles used in the AA Similarity postulate. Additionally, given that BC = BA, the triangles share angle B, providing the second angle needed to prove that the triangles are similar by AA (Angle-Angle) Similarity.
Therefore, by the AA Similarity postulate, we conclude that Triangle BDA is similar to Triangle BDC.