1. ## Parallelogram Help

Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogram is a rhombus. State your plan and give proof.

Given: ABCD is a parallelogram with angle 1 congruent to angle 2.
To Prove: ABCD is a rhombus
Plan: _________________________________________________

PROOF

Statements:__________________________________

Reasons: _____________________________________

2. Hello, whytechocolate!

I'll give you the game plan . . . you fill in the details.

Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram,
the parallelogram is a rhombus.
We know that: .AB = CD, AD = BC .(Opposite sides of a parallelogram are equal)

We need to show that two adjacent sides are equal: say, AB = BC.

We know that: .angle A = angle C. .
(Opposite angles of a parallelogram are equal)

AC bisects angles A and C.
. . Hence: /1 = /2 = /3

Since /2 = /3, triangle ABC is isosceles.

Therefore: .AB = BC