Parallelograms

1

Parallelogram2

The symbol for parallelogram is a smaller version of the figure. A parallelogram is named using all four vertices.You can start from any one vertex, but you must continue in a

clockwise or counterclockwise direction.For example, the figure above can be either ABCD or

ADCB.

Definition: A quadrilateral with both pairs of opposite sides parallel.

CB

A D

Properties of Parallelogram

3

1. Both pairs of opposite sides are congruent.

2. Both pairs of opposite angles are congruent.

3. Diagonals bisect each other but are not congruent

P is the midpoint of AC and BD, so BP = PD and AP = PC.

A B

CDP

Examples 4

Draw HKLP.

HK = _______ and HP = ________ .

m< K = m<______ .

m< L + m<______ = 180°.

If m< P = 65°, then m< H = ____, m< K = ____ and

m< L =____.

Draw the diagonals with their point of intersection labeled M.

If HM = 5, then ML = ____ .

If KM = 7, then KP = ____ .

If HL = 15, then ML = ____ .

If m<HPK = 36°, then m<PKL = _____ .

H K

LP

PL KLP

P or K

115° 65°

115°

M

5 units

14 units7.5 units

36°

(Alternate interior

angles are congruent.)

Examples5

ABCD is a parallelogram. Find the values of x, y, and z.

Example 2: In GEOM, EA = 2x2 + 5x and AM = 4x + 2. Find the value of x. What are EA and AM?

G

E

M

O

A

Example 3. Given TRAC. If TC = 3x - 5 and RA = 25, solve for x.

T R

AC

1

K

43

2

If m CTR = 2y - 13 and m ACT = y + 1. Find y.∠ ∠

Example 48