Question

In a parallebogram ABCD side AB is produced to point M and E is the mid-point of BC
Prove That (i) DCE = MBE (ii) AB= AM (iii) AM 2DC​

Answer 1

Now using the diagram we have,

(i)
angel DCE will be equal to angle MBE since AB is parallel to DC (as ABCD is a parallelogram)


(ii)
In triangle EBM and ECD
angle MBC = angle ECD (as AM || DC)

angle MEB= angel DCE ( vertically opposite angles)

and

BE =CE (as E is the midpoint of BC)

now by ASA congruence criteria both the triangles are congruent.

by CPCT we have DC = BM ---- eq (a)

since AB = DC (opposite side of a parallelogram)
we have,

AB = BM


(iii)

AM = AB + BM ---(b)

From eq (a) we have,
DC=BM
and DC = AB (equal opposite side of a parallelogram)

using these in (b)
we have,
AM = DC +DC =2DC

Hence proved.

Answer 2

Answe

Step-by-step explanation: