5.1 Properties of Parallelograms5.1 Properties of Parallelograms

Geometry

Ms. Kelly

Fall 2010

Objectives:Objectives:

• Apply the definition of a parallelogram and the theorems about properties of a parallelogram.

In this lesson . . . In this lesson . . .

And the rest of the chapter, you will study special quadrilaterals. A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

When you mark diagrams of quadrilaterals, use matching arrowheads to indicate which sides are parallel. For example, in the diagram to the right, PQ║RS and QR║SP. The symbol PQRS is read “parallelogram PQRS.”

Opposite sides of a Opposite sides of a parallelograms are parallel!!! parallelograms are parallel!!!

Duh!Duh!

Theorems about parallelogramsTheorems about parallelograms

• 5.1 Opposite sides of a parallelogram are __________.

►PQ RS and ≅SP QR≅

P

Q R

S

Theorems about parallelogramsTheorems about parallelograms

• 5.2 Opposite angles of a parallelogram are ____________.

P ≅ R andQ ≅ S

P

Q R

S

Theorems about parallelogramsTheorems about parallelograms

• 5.3 Diagonals of a parallelogram ____ each other.

QM SM and ≅

PM RM ≅

P

Q R

S

Ex. 1: Using properties of Ex. 1: Using properties of ParallelogramsParallelograms• FGHJ is a

parallelogram. Find the unknown length.

a. JH

b. JK

Answers:

a. JH =5

b. JK = 3

F G

J H

K

5

3

b.

Consecutive angles of a Consecutive angles of a parallelogram are supplementary!parallelogram are supplementary!

Ex. 2: Using properties of parallelogramsEx. 2: Using properties of parallelograms

PQRS is a parallelogram.

Find the angle measure.

a. mR

b. mQa. mR = mP

mR = 70°

b. mQ + mP = 180°

mQ + 70° = 180°

mQ = 110°

P

RQ

70°

S

a

6

b9

U T

SR

80

xy

Try it…Try it…  

If quadrilateral RSTU is a If quadrilateral RSTU is a parallelogram find the values of x, parallelogram find the values of x,

y, a, and b.y, a, and b.

Check for UnderstandingCheck for Understanding

Page 168 3-7

For numbers 5-7, only answer yes or no if it can be a parallelogram

3.

4.

5.

6.

7.

One final example…One final example…

• Find the values of x and y…

• Systems of equations!!18

2x + 8y

27

4x – 2y

Graded assignmentsGraded assignments

Worksheet Practice B collected and graded

Homework page 169-170 1-13, 19-24

Closure (on little piece of paper)Closure (on little piece of paper)

Name 5 properties of parallelograms.

1.opp. Sides are //

2.Opp. Sides are cong

3.Opp. Angles are cong

4.Diagonals bisect each other

5.Consec angles are supp