Warm UpFind the value of each variable.

1. x 2. y 3. z2 184

Sections 8-2 & 8-3

Parallelograms

•A quadrilateral with two pairs of parallel sides is a parallelogram. •To write the name of a parallelogram, you use the symbol .

What is a Parallelogram?

Properties of Parallelograms?

• Opposite sides are congruent.• Opposite angles are congruent.• Consecutive angles are

supplementary.• If a has one right angle, then it

has 4 right angles.

What about the diagonals?• The diagonals of a

parallelogram bisect each other.

• Each diagonal of a parallelogram separates the parallelogram into 2 congruent triangles.

In CDEF, DE = 74 mm, DG = 31 mm, and mFCD = 42°. Find CF.

CF = 74 mm

Applying Properties of Parallelograms:

Find mEFC mEFC = 138°

Find DF DF = 62

Example: Using Properties of Parallelograms to Find Measures

WXYZ is a parallelogram. Find YZ.

YZ = 52

Find mZ .

mZ = 65

Example:

EFGH is a parallelogram.Find JG.

JG = 12

Find FH.

FH =18

Lesson Quiz: Part I

In PNWL, NW = 12, PM = 9, and mWLP = 144°. Find each measure.

1. PW 2. mPNW

18 144°

Lesson Quiz: Part II

QRST is a parallelogram. Find each measure.

2. TQ 3. mT

28 71°

Area of a Parallelogram?

Find the area of the parallelogram.

A = 176 mm2

Example:

Find the base of the parallelogram in which h = 56 yd and A = 28 yd2.

b = 0.5 yd

To prove a quadrilateral is a parallelogram, use any one of these conditions:

Example: Applying Conditions for Parallelograms

Determine if the quadrilateral must be a parallelogram. Justify your answer.

No. Only one pair of opposite angles are congruent.

Example:

Determine if the quadrilateral must be a parallelogram. Justify your answer.

The diagonal of the quadrilateral forms 2 congruent triangles.

Yes

Example:

Determine if each quadrilateral must be a parallelogram. Justify your answer.

No.

None of the sets of conditions for a parallelogram are met.

To Prove Parallelograms on the

Coordinate Plane:• Given vertices as ordered pairs.

Compare Slopes

Slopes and Distance Formula

Use Midpoint Formula

No; One pair of consecutive s are , and one pair of opposite sides are ||. The conditions for a parallelogram are not met.

Lesson Quiz

1. Show that JKLM is a parallelogram for a = 4 and b = 5.

2. Determine if QWRT must be a parallelogram. Justify your answer.

JN = LN = 22; KN = MN = 10; so JKLM is a parallelogram by Theorem 6-3-5.