Question

In right triangle ABC, the right angle is at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point) B (see figure).

State whether the statement is true/false

$\Delta AMC\cong \Delta BMD$

• A. True
• B. False

Answer 1

The correct option is A True

$In△AMC\&△DMB$

$AM=MB=x$(given)

$DM=CN=y$ (given)

$\angle DMB=\angle AMC$ (vertically opposite)

$\therefore △AMC\cong △DMB$ (by S.A.S)