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Answer:
use the definition of isosceles to claim congruent sides (or angles), and use the shared side and the fact that angles at C are 90°. Claim HL or AAS congruence.
Explanation:
Approach to the problem
Of course, AC is congruent to itself. AC ⊥ BD means ∠ACB ≅ ∠ACD ≅ 90°. Then the fact that the larger triangle is isosceles lets you claim angle B = angle D, or AB = AD (or both).
If you use the congruence of angles, you can claim AAS congruence for the triangles. If you use the congruence of sides, you can claim HL congruence for the right triangles.
Specifics
1. ∠ACB ≅ ∠ACD (= 90°) . . . . definition of perpendicular
2. AB ≅ AD . . . . definition of isosceles triangle
3. AC ≅ AC . . . . reflexive property of congruence
4. ∆BAC ≅ ∆DAC . . . . HL congruence theorem