Question

In the given figure, ABCD is a parallelogram. M is the midpoint of BD and BD
bisects B as well as D. find the measure of AMB.

Answer 1

Given :  ABCD is a parallelogram. M is the midpoint of BD

BD bisects ∠B and ∠D

To Find : the measure of ∠AMB.

Solution:

ABCD is a parallelogram

=> ∠B = ∠D  ( opposite angles of parallelogram are equal )

BD bisects ∠B and ∠D

=> ∠ADB = ∠ABD

=> AB = AD   ( opposite sides of Equal angles)

∠ADB = ∠ABD

=> ∠ADM = ∠ABM  as M lies on BD

and BM = DM as M is  mid point of BD  

in  ΔADM  and  ΔABM

AD = AB  ( shown above)

∠ADM = ∠ABM

DM = BM

=> ΔADM  ≅  ΔABM

=> ∠AMD = ∠AMB

∠AMD + ∠AMB = 180°  ( Linear Pair)

=> 2 ∠AMB = 180°  

=>  ∠AMB = 90°  

the measure of ∠AMB is 90°  

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