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ABCD is a rhombus. Show that diagonal AC bisects A as well as C and diagonal BD bisects B as well as D.

Asked by Topperlearning User 4th June 2014, 1:23 PM
Answered by Expert
Answer:

Let us join AC.

In ABC,

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.

Answered by Expert 4th June 2014, 3:23 PM
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