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Mathematics
Mathematics
Problem
In parallelogram
A
B
C
D
ABCD
A
B
C
D
, diagonal
A
C
AC
A
C
is drawn. It is given that
A
B
=
5
cm
AB = 5\,\text{cm}
A
B
=
5
cm
,
B
C
=
4
cm
BC = 4\,\text{cm}
B
C
=
4
cm
and
∠
A
B
C
=
60
∘
\angle ABC = 60^{\circ}
∠
A
B
C
=
6
0
∘
. (i) Prove that
△
A
B
C
≅
△
C
D
A
\triangle ABC \cong \triangle CDA
△
A
B
C
≅
△
C
D
A
. (ii) Find the measure of
∠
C
D
A
\angle CDA
∠
C
D
A
. (iii) Determine the length of
C
D
CD
C
D
. (iv) Calculate the perimeter of the parallelogram
A
B
C
D
ABCD
A
B
C
D
.
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