Question

WILL MARK YOU BRAINLIEST, PLEASE HELP!!!

Answer 1

Given:ABCD is a rhombus.

To prove:DE congruent to BE.

In rombus, we know opposite angle are equal.

so, angle DCB = angle BAD

SINCE, ANGLE DCB= BAD

SO, In triangle DCA

angle DCA=angle DAC

similarly, In triangle ABC

angle BAC=angle BCA

since angle BCD=angle BAD

Therefore, angle DAC =angle CAB

so, opposite sides of equal angle are always equal.

so,sides DC=BC

Now, In triangle DEC and in triangle BEC

1. .DC=BC (from above)............(S)

2ANGLE CED=ANGLE CEB (DC=BC)....(A)

3.CE=CE (common sides)(S)

Therefore,DE is congruent to BE (from S.A.S axiom)