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Mathematics
Problem
A student wishes to prove that quadrilateral
A
B
C
D
ABCD
A
B
C
D
is a parallelogram. Which one of the following single statements, if known to be true, is by itself adequate for the proof? a)
∠
A
+
∠
B
=
180
∘
\angle A + \angle B = 180^{\circ}
∠
A
+
∠
B
=
18
0
∘
b)
∠
A
=
∠
D
\angle A = \angle D
∠
A
=
∠
D
c)
∠
A
=
∠
C
and
∠
B
=
∠
D
\angle A = \angle C \,\text{and}\, \angle B = \angle D
∠
A
=
∠
C
and
∠
B
=
∠
D
d)
∠
A
+
∠
C
=
180
∘
\angle A + \angle C = 180^{\circ}
∠
A
+
∠
C
=
18
0
∘
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