Final answer:
To prove that triangle ABD is congruent to triangle CBD, we use the right angles formed by AC perpendicular to BD and the congruence of sides AB and BC, applying the Hypotenuse-Leg (HL) congruence theorem.
Step-by-step explanation:
The question seems to be asking about the properties of geometric figures and the relations between angles, sides, and triangles. However, most of the information provided is not directly relevant to the question posed, which concerns proving that triangle ABD is congruent to triangle CBD under certain conditions. To prove this congruence, we would use the fact that AC⊥BD means angle ACD is a right angle, and so is angle BCD since they share side CD, and if AB≅BC, those are two equal sides of the triangles in question. Since both triangles share side BD and both have a right angle, by the Hypotenuse-Leg (HL) congruence theorem for right triangles, triangle ABD is indeed congruent to triangle CBD.