Q. 64.3( 11 Votes )

# ABC is a triangle

Given:- ACB is right angle triangle

M is midpoint of AB

DM||CB

Formula used:- Line drawn through midpoint of one side of triangle

Parallel to other side , bisect the 3rd side

* SAS congruency property

If 2 sides and angle between the two sides of both

the triangle are equal, then both triangle are congruent

Solution:-

(1) In Δ ABC

M is midpoint of AB

And DM||CB

D is midpoint of AC

Line drawn through midpoint of one side of triangle

Parallel to other side , bisect the 3rd side

(2) In Δ ABC

DM||CB

ADM= ACB [Corresponding angles]

ACB =90°

(3) In Δ ADM and Δ DMC

DM=DM [Common in both triangles ]

AD=DC [D is the midpoint]

As ADC is straight line

MDC=90°

Hence;

In Δ ADM Δ DMC

CM=MA

MA=AB [M is midpoint of AB]

CM=MA=AB

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