chapter 6 review

Chapter 6 ReviewThis is a review over all the stuff that you have learned, or should have learned, in chapter 6.

Types of Special Quadrilaterals

ParallelogramsRectanglesRhombus (Rhombi)SquaresTrapezoids

Properties for ParallelogramsBoth pairs of opposite sides are parallel and congruentDiagonals bisect each otherOpposite angles are congruentConsecutive angles are supplementary

DRAW A PARALLELOGRAM

ParallelogramA

E

B

D C

Tests for Parallelograms• If one pair of opposite sides are parallel and

congruent, then it is a parallelogram• If both pairs of opposite sides are parallel, then

it is a parallelogram• If both pairs of opposite sides are congruent,

then it is a parallelogram• If both pairs of opposite angles are congruent,

then it is a parallelogram• If diagonals bisect each other, then it is a

parallelogram

Properties of a RectangleBoth pairs of opposite sides are parallel and congruentDiagonals bisect each otherOpposite angles are congruentConsecutive angles are supplementary All four angles are rightDiagonals are congruent

DRAW A RECTANGLE

Rectangles: If <DAE = 30 degrees can you determine the remaining angles?

A

D C

B

E

Tests for Rectangles

• If a quadrilateral has four right angles, then it is a rectangle

• If a parallelogram has congruent diagonals, then it is a rectangle

Properties for a RhombusBoth pairs of opposite sides are parallel and congruentDiagonals bisect each otherOpposite angles are congruentConsecutive angles are supplementaryDiagonals intersect at 90 degree anglesEach diagonal bisects opposite anglesAll sides are congruent

Rhombi: If <BAE = 25degrees can you determine the other angles?

BD

CB

A

E

Tests for Rhombi

• If the diagonals of a parallelogram are perpendicular, then it is a rhombus

Properties of SquaresBoth pairs of opposite sides are parallel and congruentDiagonals bisect each otherOpposite angles are congruentConsecutive angles are supplementaryAll four angles are rightDiagonals are congruentDiagonals intersect at 90 degree anglesEach diagonal bisects opposite anglesAll sides are congruent

Squares

A

A B

CD

E

Tests for Squares

• If a quadrilateral is a rectangle and a rhombus, then it is a square

Trapezoids• Bases

• Legs

• Median

Isosceles Trapezoid

A B

CD

M E

• Get out a clean sheet of paper– Label it Chapter 6 Review– Complete each following slide on that paper

• ABCD is a rectangle <A = 3x + 4 find x

• ABCD is a parallelogram <A = 2x + 12 <B = 3x + 8

• To prove that a quadrilateral is a parallelogram you must show that the diagonals ________________________________________

ABCD is a parallelogram <ABC = 52 <BCD = ?

AD = 3x + 25, BC = 5x + 11 Find x, AD <EBC = 2x + 12, <ADE = 3x + 8 Find x

A

EB

D C

Rhombi: If <BAE = 30degrees can you determine the other angles? Draw and

completeB

D

CB

A

E

Rhombus If <BEA = 5x + 15 Find x

If AD = 15 and BC = 3x + 9 Find xB

D

CB

AE

Write the formula

•Midpoint Formula•Distance Formula• Slope

• Explain in words how to show if four points create a parallelogram, a rectangle, a rhombus, and/or a square

Define Each Term• Alternate Interior• Parallelogram• Rectangle• Rhombus• Square• Isosceles Trapezoid