Question

ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Fig. 7.17). Prove that: ∠ABD=∠BAC. bd=ac ,abd=bac​

Answer 1

Step-by-step explanation:

construction =draw line AC And BD.

now in triangle ABD And ABC

AB = AB. common

AD = BC. given

angle DAB = angle CBA given

thus angle ABD= BAC

Answer 2

Given : ABCD is a quadrilateral AD = BC and ∠DAB = ∠CBA

To prove :

1. △ABD ≅△BAC
2. BD = AC
3. ∠ABD = ∠BAC

Proof : In △ABD and △BAC

AD = BC ( Given)

AB = AB ( common )

∠DAC = ∠CBA ( Given)

Therefore, by SAS congruence △ABD ≅△BAC

2. Since △ABD ≅△BAC

Therefore, by CPCT BD = AC

3. Since △ABD ≅△BAC

Therefore, by CPCT ∠ABD = ∠BAC

Proved