ABCD is a rhombus. Show that diagonal AC bisects A as well as C and diagonal BD bisects B as well as D.
Let us join AC.
BC = AB (Sides of a rhombus are equal to each other)
1 = 2 (Angles opposite to equal sides of a triangle are equal)
However, 1 = 3 (Alternate interior angles for parallel lines AB and CD)
2 = 3
Therefore, AC bisects C.
Also, 2 = 4 (Alternate interior angles for || lines BC and DA)
1 = 4
Therefore, AC bisects A.
Similarly, it can be proved that BD bisects B and D as well.
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