Question

If M is the midpoint of AB in rectangle ABCD , prove that triangle AMD = triangle BMC​

Answer 1

Given:-
ABCD is a rectangle,
M is the midpoint of AB.
To prove:-
AMD=BMC
Proof:-
In AMD and BMC
AM=BM (M is the midpoint of AB) (S)
Angle DAM= Angle CBM (Angles in a rectangle) (A)
AD=BC (Opposite sides in a rectangle are equal) (S)
Therefore, by SAS congruence
AMD congruent to BMC
ie.,AMD=BMC
Hence proved.