Question

3.If ABCD is a parallelogram with AB = 2x + 1, AD = x + 13, and DC = 3x -11. Determine if ABCD is

rhombus. Show algebraic work to justify your answer.

Answer 1

ABCD is a rhombus

Explanation:

Sides AB and DC are opposite and equal in parallelogram ABCD. This means ...

AB = CD

2x +1 = 3x -11

12 = x . . . . . . . . add 11-2x to both sides

Sides AB and CD have length ...

2x +1 = 2(12) +1 = 24 +1 = 25

Then the length of side AD is ...

AD = x +13 = 12 +13 = 25

Adjacent sides AB and AD of the parallelogram have the same length, The figure is a rhombus.