Question

ABCD is a quadrilateral in which AD = BC and
<DAB = <CBA Prove that

(1 ) TRIANGLE ABD=TRIANGLE BAC
(2) BD=AC
(3) <ABD= <BAC.
​

Answer 1

Step-by-step explanation:

Given : AD =BC

and < DAB = <CBA

To proof : ∆ABD =∆BAC , BD = AC , <ABD =<BAC

Proof : In ∆ABD and ∆ BAC ,

AD = BC ( given )

<DAB = < CBA (given )

AB = BA ( common )

∆ABD =∆BAC ( SAS congruence rule )

BD =AC ( CPCT )

And , <ABD = BAC ( CPCT )