Geometry: Proof

Use the definitions of the isoceles triangle MAD. That is side segments AD=AM and angles AMD=ADM.

Now draw a segment AN that is the altitude of the triangle MAD from the vertex A to a point N on the segment N on the base segment MD, such that AN is perpindicular to MD (definition of altitude).

You've then created two right triangles MAN and NAD, and in the right triangles segments AD=AM, AN=AN and angles ANM=AND, moreover angles AMN=ADN--so the triangles MNA and AND are congruent.

So segments MN and ND are equal.

Since MN=ND and MN+ND=MD then MN=ND=MD/2 and N is the midpoint of MD.

Rap

thank u so much..that helped a lot!