chapter 5 review. + definition a parallelogram is a quadrilateral with both pairs of opposite sides...

Chapter 5 Review

+Definition

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

A B

D C

ABCDNOTATION

+Sides - Paralleogram

Opposite sides are congruent

Opposite sides are parallel

+TheoremOpposite angles of a parallelogram are congruent

Consecutive angles are supplementaryA B

D C

103

10377

77

+Theorem

Diagonals of a parallelogram bisect each other.

A B

D C

+DefinitionA rectangle is a quadrilateral with four right angles.

+Rectangle

Opposite sides are congruent

Opposite sides are parallel

Sides

AnglesFour right angles

+Recall that a rectangle is a parallelogram.

Therefore a rectangle has all the same properties that a Parallelogram has! A rectangle also has some unique properties.

A Rectangle:The diagonals bisect each other

The diagonals are congruentUnique Properties

+

The diagonals of a rectangle are congruent.

CT

ER

RC = ET

Rectangle Properties

+Definition - RhombusA quadrilateral with four congruent sides.

+Rhombus

All sides are congruent

Sides

AnglesOpposite angles are congruent

Consecutive angles are supplementary

+

A Rhombus:The diagonals bisect each other

The diagonals are perpendicular

Unique Properties

Each diagonal of a rhombus bisects two angles of the rhombus

Recall that a rhombus is a parallelogram.

Therefore a rhombus has all the same properties that a Parallelogram has! A rhombus also has some unique properties.

+Definition - SquareA quadrilateral with four right angles and four congruent sides.

+Square

All sides are congruent

Sides

AnglesAll are right angles

+A Square can also be defined as a………..

A Square: The diagonals bisect each other

The diagonals are congruent

Parallelogram Rectangle Rhombus

The diagonals are perpendicular

Each diagonal of a square bisects two angles of the square

+Definition

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

The parallel sides are called the bases

The other sides are called the legs

+Definition

An isosceles trapezoid is a trapezoid with congruent legs.

THEOREM: Base angles of an isosceles trapezoid are congruent

BASE

BASE

If trapezoid ABCD has AB = DC, then<A = <D and <B = <C

A

B

D

C

+TheoremIf both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

A B

D C

10

10

7 7

+TheoremIf both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram

A B

D C

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

A B

D C

10

10

+TheoremIf both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogramA B

D C

103

10377

77

+TheoremIf the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. A B

D C

+THEOREM

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.

A

CB

X

If ABC has right <ABC and X is the midpoint of AC, then

BX = AX = XC

5

55

+THEOREM

The median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths.

6 cm

10 cm

Median = (6+10)/2

Median = 16/2

Median = 8 cm8 cm

+THEOREM

If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

+THEOREM

A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side.

+TheoremThe segment that joins the midpoints of two sides of a triangle is half as long as the third side.N

A C

ED 10

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