Q. 64.3( 11 Votes )

ABC is a triangle

Answer :

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


AD=DC


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°


ADM=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


ADM+ MDC=180°


MDC=180° - ADM


MDC=90°


ADM= MDC


Hence;


In Δ ADM Δ DMC


CM=MA


MA=AB [M is midpoint of AB]


CM=MA=AB


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