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5 votes
Complete the proof.
Given: AD || BC, AB ||CD
Prove: <B = <D


1 Answer

7 votes

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

.

User Betohaku
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