Chapter 6 Quadrilaterals Thompson Parallelogram – both pairs of opposite sides are parallel Rhombus – four congruent sides Special Quadrilaterals.

• Chapter 6• Quadrilaterals• Thompson

Parallelogram – both pairs of opposite sides are parallel

Rhombus – four congruent sides

Special Quadrilaterals

Rectangle – four right angles Square – four congruent sides and four congruent angles

Kite – two pairs of adjacent sides are congruent and no opposite sides are congruent

Trapezoid – Exactly one pair of parallel sides Isosceles Trapezoid – the nonparallel

sides are congruent.

Classifying a Quadrilateral

Judging by appearance, classify ABCD in as many ways as possible.

Quadrilateral and Trapezoid

Relationships Among Special Quadrilaterals

Quadrilateral

No parallel sides

Kite Trapezoid

One pair of parallel sides

Isosceles Trapezoid

Parallelogram

Rectangle Rhombus

Square

Two pairs of parallel sides

Using the Properties of Special Quadrilaterals

In parallelogram RSTU, m R = 2x – 10 and m S = 3x + 50. Find x.

Closing . . .

ABCD is a square. Which classifications from this lesson apply to a square? Which do not apply?

A square is:

A square is not:

quadrilateral, parallelogram, rectangle, rhombus

trapezoid, kite

Classifying Quadrilaterals

Directions:• When the slide appears say the best name for the quadrilateral aloud.

• Try to beat the computer by saying the answer before the computer in 4 seconds.

Best Name:

Isosceles

Trapezoid

Best Name:

Best Name:

SquareBest Name:

This quadrilateral is also:

• a rectangle • a rhombus• a parallelogram

Best Name:

QuadrilateralBest Name:

Best Name:

RhombusBest Name:

This quadrilateral is also:

• a parallelogram

Best Name:

QuadrilateralBest Name:

Best Name:

RectangleBest Name:

This quadrilateral is also:

• a parallelogram

Best Name:

Isosceles

Trapezoid

Best Name:

Best Name:

RhombusBest Name:

This quadrilateral is also:

• a parallelogram

Best Name:

ParallelogramBest Name:

Best Name:

TrapezoidBest Name:

Best Name:

QuadrilateralBest Name:

Best Name:

ParallelogramBest Name:

Best Name:

TrapezoidBest Name:

Best Name:

RectangleBest Name:

This quadrilateral is also:

• a parallelogram

Best Name:

RhombusBest Name:

This quadrilateral is also:

• a parallelogram

Best Name:

SquareBest Name:

This quadrilateral is also:

• a rectangle • a rhombus• a parallelogram

Best Name:

2nd Stellation

Of Icosododecahedron

Game Over!

Classwork

Page 290#’s 1-12, 19, 22, 23, 29-34, 37-42, 55

LESSON 6-2

Properties of Parallelograms

Key to remembering these!

We’re going to be learning a lot of similar looking theorems.

Draw a few pictures to see what happens.

Thm 6-1

Opposite sides of a parallelogram are congruent.

Other Properties of Parallelograms: Opposite sides are parallel Consecutive angles are supplementary

Using Consecutive Angles

Use parallelogram KMOQ to find m O.

m O = 145

Thm 6-2

Opposite angles of a parallelogram are congruent.

Thm 6-3

The diagonals of a parallelogram bisect each other.

Using Thms. 6-1 and 6-2

Find the value of x in parallelogram ABCD. Then find m A.

m A = 105

Example 1

Find the values of x and y.

Example 2

Find each indicated measure.1. NM2. KM3. mJKL4. mLKM

Thm 6-4

If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

LESSON 6-3

Proving That a Quadrilateral is a

Parallelogram

Thm 6-5

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Thm 6-6

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

Finding Values for Parallelograms

Find values of x and y for which ABCD must be a parallelogram.

x = 18 and y = 89

Thm 6-7

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Thm 6-8

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Is the Quadrilateral a Parallelogram?

Determine whether the quadrilateral is a parallelogram. Explain.

Classwork

Page 297#’s 18, 20, 40, 43, 46, 47 Page 307 #’s 7-15, 32-34