Prove the following:

Question

Given: AD = BD and AC = BD

Prove: Angle CAD is congruent to Angle CBD

Given: AC = BC; Angle CAD is congruent to Angle CBD

Prove: AD = BD

Diagram:

Triangle ACB is congruent to Angle ADB, A is congruent to B, and C is congruent to D. (I cannot insert pictures instead I explain the diagram)

Answer 1

Then Trianble CDA is congruent to triangle CDB by SSS;

the proof follows by CPCTC

The second proof follows by dropping the perpendicular height

from C to D. They are congruent isoceles right triangles