*Quadrilateral

I have exactly four sides and angles.

If you add all of my angles together, then you would

have 3600

                   

                        

*TrapezoidI have only one set of

parallel sides. 

                                         

         

*ParallelogramI have:

- 2 sets of parallel sides- 2 sets of congruent

sides- opposite angles

congruent- consecutive angles

supplementary

                               

          

*RectangleI have all of the properties of the

parallelogram PLUS- 4 right angles

                     

    

*RhombusI have all of the properties of the

parallelogram PLUS- 4 congruent sides

                           

       

*SquareHey, look at me!I have all of the properties of the

parallelogram AND the rectangle AND the

rhombus.I have it all!

         Examples

3. If one angle of a parallelogram is 60 degrees, find the number of

 degrees in the remaining 3 angles.

                                                                            

1 2

3

3. If one angle of a parallelogram is 60 degrees, find the number of

 degrees in the remaining 3 angles.

                                                                            

Since consecutive angles are supplementary, angle 1 and 600 must add up to 1800. Angle 2 is opposite of 600, therefore angle to is equal to 600. Angle 3 is opposite of angle 1, therefore angle 1 and angle 3 are congruent.

1 2

3

3. If one angle of a parallelogram is 60 degrees, find the number of

 degrees in the remaining 3 angles.

                                                                            

Since consecutive angles are supplementary, angle 1 and 600 must add up to 1800. Angle 2 is opposite of 600, therefore angle to is equal to 600. Angle 3 is opposite of angle 1, therefore angle 1 and angle 3 are congruent.

1 2

3

Angle 1 = 1200

Angle 2 = 600

Angle 3 = 1200

4. Find the number of degrees of each angle in the quadrilateral.

2x

x x

2x

4. Find the number of degrees of each angle in the quadrilateral.

2x

x x

2x

All quadrilaterals have 3600. So, x + x + 2x + 2x = 360 6x = 360 x = 60

4. Find the number of degrees of each angle in the quadrilateral.

2x

x x

2x

All quadrilaterals have 3600. So, x + x + 2x + 2x = 360 6x = 360 x = 60

Angle A = 1200

Angle B = 600

Angle C = 600

Angle D = 1200

B

D

C

A

PracticeProblems

Which statements describe the properties of a trapezoid?  

a.  The bases are parallel.b.  The diagonals are congruent.c.  The opposite angles are congruent.d.  The base angles are congruent.

Which statements describe the properties of a rhombus?

a.  The diagonals are perpendicular.b.  The diagonals are congruent.c.  The diagonals bisect each other.d.  The diagonals bisect the angles.

If one angle of a parallelogram is 60 degrees, find the

number of degrees in the

remaining 3 angles.

In rhombus MATH, MA = y + 8 and AT = 4y - 7.   

Find MA.