Question

Complete the proof.Given: AD || BC, AB ||CDProve: <B = <D​

Answer 1

A

B

=

C

D

---------------- already given

A

D

=

B

C

---------------- already given

and  

A

C

=

A

C

---------------- common

Hence  

Δ

A

B

C

≡

Δ

A

C

D

∴

∠

D

A

C

=

∠

B

C

A

- both opposite equal sides  

D

C

and  

A

B

, and

∴

C

D

||

A

B

- as alternate angles are equal

∴

∠

D

C

A

=

∠

C

A

B

- both opposite equal sides  

A

D

and  

B

C

∴

A

D

||

B

C

- as alternate angles are equal

As opposite sides of quadrilateral are parallel,

A

B

C

D

is a parallelogram.

Q

.

E

.

D

.