MATH SOLVE

3 months ago

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

Accepted Solution

A:

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
.