Find the measure of angle number 6.

50o

Properties of Parallelograms and Special Parellograms

5.5-6

Investigate ParallelogramUsing the lines on a piece of line paper as a

guide, draw a pair of parallel lines that are at least 6 cm apart. Using the parallel edges of your double-edged straightedge, make a parallelogram. Label your parallelogram LOVE.•Let’s look at the opposite angles. Measure

the angles of parallelogram LOVE. Compare a pair of opposite angles using patty paper or your protractor.

What did you notice?

Let’s look at the opposite sides of parallelogram LOVE. Compare the lengths of the opposite sides of the parallelogram you made.

Find the sum of the measures of each pair of consecutive angles in parallelogram LOVE.

Finally, let’s consider the diagonals of the parallelogram. Construct the diagonals LV and EO. Label the point where the two diagonals intersect point M. Measure LM and VM. What can you conclude about point M? Is this conclusion also true for diagonal EO? How do they relate?

The opposite angles of a parallelogram are _____________.

The consecutive angles of a parallelogram are _____________.

The opposite sides of a parallelogram are ______________.

The diagonals of a parallelogram _________________.

congruent

supplementary

parallel and congruent

bisect each other

Find the slope of: (4,6) and (-1, 9)

€

m =9 −6−1−4

m =3−5

€

m =6−9

4 −(−1)

m =−35

Be sure to have:scissorsprotractorruler

We will investigate rhombus, square, rectangle and kite.

Rhombus – equilateral parallelogramAll 4 sides are _______________.The diagonals are ______________, and

they ________________________.The diagonals of a rhombus

_____________ the angles of the rhombus.

congruentperpendicular

bisect each otherbisect

Rectangle – parallelogram with 4 right anglesThe diagonals of a rectangle are

________________ and ___________________.congruent bisect each other

Square – parallelogram with 4 right angles and 4 congruent sidesThe diagonals of a square are

________________, ________________ and ___________________.

congruentbisect each otherperpendicular

Kite – two pairs of consecutive congruent sidesThe diagonals are

____________________.Exactly one pair of ________________

angles are __________________.

perpendicularopposite

congruent