# Q: 7  ABCD is a rhombus. Show that diagonal AC bisects as well as and diagonal BD bisects as well as .

AD = CD          (ABCD is a rhombus)

3=1.................1(angles opposite to equal sides are equal )

3=2.................2 (alternate angles)

From 1 and 2, we have

1=2.................3

and        1=4.................4 (alternate angles)

From 1 and 4, we get

3=4.................5

Hence, from 3 and 5, diagonal AC bisects angles A as well as angle C.

AD = AB          (ABCD is a rhombus)

5=7.................6(angles opposite to equal sides are equal )

7=6.................7 (alternate angles)

From 6 and 7, we have

5=6.................8

and        5=8.................9(alternate angles)

From 6 and 9, we get

7=8.................10

Hence, from 8 and 10, diagonal BD bisects angles B as well as angle D.

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