Question

Somebody please help me with this problem!??

Answer 1

5.

We are given that AB ≅ CB and AD ≅ CD.

We know that BD ≅ BD, so ΔABD ≅ ΔCBD by SSS.

Then ∠1 ≅ ∠2 by CPCTC; and ∠3 ≅ ∠4, also by CPCTC.

Since ∠1 ≅ ∠2, BD is the bisector of (∠1+∠2) = ∠ABC.

Since ∠3 ≅ ∠4, BD is the bisector of (∠3+∠4) = ∠ADC.

6.

From (5), we know BD is the angle bisector of ∠ABC. ΔABC is isosceles, so the bisector of the apex angle is also an altitude and median. That is, point M on BD and AC must be the midpoint of AC by the definition of a median.