Q. 74.0( 404 Votes )

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

Answer :

Let us join AC.

To Prove: ∠1 = ∠4, ∠2 = ∠3
Proof:

In ΔABC,

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

Hence, Proved.

Similarly, it can be proved that BD bisects B and D as well.

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