Question

9. In the given figure, the line segments AB and CD intersect at
a point M in such a way that AM MD and CM = MB. Prove
that, AC = BD but AC may not be parallel to BD.
[Hint. Angle MAC = Angle MDB. So, Angle MDB
Angle MAC.
Thus, Angle MDB + Angle MCA.]​

Answer 1

Answer:

given:

AM = BM

CM = MB

angle AMC = angle DMB ( AB intersect CD , vertically opposite angles)

therefore by side angle side criterion

triangle AMC is congruent to triangle DMB

by cpct :

AC = BD but AC may not be parallel to BD