The prove, angle BAC is congruent to angle BCA. and AM perpendicular to MD is achieved using SAS congruence theorem, Isosceles triangle theorem and properties of kite
How to complete the proof
The two column proof is written as follows
Statement Reason
∠ ADB ≅ ∠ CDB given
AD ≅ DC given
DB ≅ BD Reflexive property
Δ ADB ≅ Δ CDB SAS congruence theorem
BA ≅ BC CPCTC
ABCD is a kite Two pairs of adjacent sides equal
∠ BAC ≅ ∠ BCA Isosceles triangle theorem
AM ⊥ MD Diagonals of kite bisect each other