1 / 8

# Parallelograms - PowerPoint PPT Presentation

Parallelograms. B. C. D. A. Parallelogram. Definition:. A quadrilateral with both pairs of opposite sides parallel. The symbol for parallelogram is a smaller version of the figure. A parallelogram is named using all four vertices.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Parallelograms' - jonco

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

C

D

A

Parallelogram

Definition:

A quadrilateral with both pairs of opposite sides parallel.

• 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

B

Properties of Parallelogram

P

D

C

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.

Examples

K

M

P

L

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 = _____ .

PL

KL

P

P or K

115°

65°

115°

5 units

(Alternate interior

angles are congruent.)

14 units

7.5 units

36°

• 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

M

A

E

O

T

R

3

4

K

1

2

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

C

A

Example 4 solve for x.