ABCD is a rhombus. Show that diagonal AC bisects
as well as
and diagonal BD bisects
as well as
.
Solution:
ABCD is a rhombus. We need to prove that AC bisects
and
. Also, BD bisects
and
.
In
and
BC=DC (Sides of rhombus are equal)
BA=DA (Sides of rhombus are equal)
AC=AC (Common)
Therefore, by SSS congruence rule,
(Corresponding parts of congruent triangles are equal) (1)
And,
(Corresponding parts of congruent triangles are equal) (2)
From (1) and (2), we can say that diagonal AC bisects
and
.
Similarly, BD bisects
and
.
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