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Mathematics
Mathematics
Problem
In quadrilateral
A
B
C
D
ABCD
A
B
C
D
it is given that
A
B
=
C
D
AB = CD
A
B
=
C
D
and
∠
B
A
D
=
∠
A
D
C
\angle BAD = \angle ADC
∠
B
A
D
=
∠
A
D
C
. (i) Prove that
A
B
∥
C
D
AB \parallel CD
A
B
∥
C
D
. (ii) Hence, show that
A
B
C
D
ABCD
A
B
C
D
is a parallelogram. (iii) If
A
B
=
C
D
=
7
cm
AB = CD = 7\,\text{cm}
A
B
=
C
D
=
7
cm
and
A
D
=
5
cm
AD = 5\,\text{cm}
A
D
=
5
cm
, find the perimeter of
A
B
C
D
ABCD
A
B
C
D
.
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