Properties of Rhombus, Rectangles, and Kites.

Learning Target: I can define and classify special types of parallelograms.

Each diagonal of a rhombus bisects two angles ofthe rhombus.

If one diagonal of a parallelogram bisects two anglesof the parallelogram, then the parallelogram is arhombus.

The diagonals of a rhombus are perpendicular.

If the diagonals of a parallelogram are perpendicular,then the parallelogram is a rhombus.

MNPQ is a rhombus and m<N=120. Find the measures of the numbered angles.

1200

N

M

1

2

3

4

P

Q

30

The diagonals of a rectangle are congruent.

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

A

B

C

D

AD≅BC

Examples1. MNPQ is a rhombus and m<N=140. Find m<4.

2. Find the length of the diagonals if FD=2y+4 andGE=6y+5.

N

M

P

4

Q

F

G

E

D

4=20

2y+4=6y+5-4y+4=5-4y=1y=-1/4

FD=2y+4FD=2(-1/4)+4FD=3.5

GE=6y+5GE=6(-1/4)+5GE=3.5