Question

Point D is in the interior of △ABC. Line CD intersects AB at point M. Prove that, if AADC=ABDC, then CM is the median of △ABC.

Answer 1

Answer:

Proved

Step-by-step explanation:

Given that in a triangle ABC, a line Starting from vertex C through an interior point M meets the opposite side AB at the point D.

Also given that areas of ADC and BDC are equal.

We find that ADC and BDC are triangles with bases as the same line.  Hence altitude dropped from C would have the same height for both triangles

In other words, heights are equal.

ARea of triangle ADC = Area of triangle BDC

$1/2 (AD) (h) = 1/2 (BD)(h)\\AD =BD$

It follows D is the mid point of AB.

Or CM is the median of ABC