Question

In figure, AE=BE and angle C = angle D. Prove AD=BC ​

Answer 1

Given: in given figure AE=BE and angle C=angle D

To prove: AD=BC

solution : In ∆AEC and ∆BED

angle C= angle D (given)

AE=EB(given)

angle AEC =angle BED(v.opp.angle)

so, ∆AEC and ∆BED are congruent by AAS

hen, CE=ED (c.p.c.t)_______{1}

Now adding AD both side in {1}

CE+AD=ED+AD (also AD=BE)

so,CE+BE= ED+AD

BC=AD ......(Hence proved)

Answer 2

Answer:

in ΔAEC and ΔBED

__AE = BE....given

__<AEC =<BED.....vertically opp angles

__<C = <D.....given

therefore ΔAEC and ΔBED are congruent

.

therefore proved