* quadrilateral i have exactly four sides. *trapezoid i have only one set of parallel sides. [the...

*Quadrilateral

I have exactly four sides.

*TrapezoidI have only one set of

parallel sides. [The median of a

trapezoid is parallel to the bases and equal to one-half the sum of the

bases.]

Isosceles TrapezoidI have:- only one set of parallel sides- base angles congruent- legs congruent- diagonals congruent- opposite angles supplementary

ParallelogramI have:- 2 sets of parallel sides- 2 sets of congruent sides- opposite angles congruent- consecutive angles supplementary- diagonals bisect each other- diagonals form 2 congruent triangles

TRAPEZOIDS-quadrilateral with one pair of parallel sides

TRAPEZOIDS

-parallel sidesbases

TRAPEZOIDS

-pair of angles that share a basebase angles

TRAPEZOIDS

-pair of angles that share a basebase angles

Open books to page 291. Work on investigation 6.3.2 on your own.

Trapezoid Consecutive Angles Conjecture

The consecutive angles between the bases of a trapezoid are ______________. supplementary

TRAPEZOIDSm1 + m2 =180°

m3 + m4 =180°

TRAPEZOIDS

-two nonparallel sides are congruent

isosceles trapezoid

Isosceles Trapezoid Conjecture

The base angles of an isosceles trapezoid are ______________. congruent

TRAPEZOIDSm1 = m4

m2 = m3

Isosceles Trapezoid Diagonals Conjecture

The diagonals of an isosceles trapezoid are ______________.

congruent

TRAPEZOIDSmAC = mBD

Properties of Parallelograms

Objectives:

1. Discover properties of parallelograms.

parallelogram: -quadrilateral whose opposite sides are parallel

ParallelogramI have:- 2 sets of parallel sides- 2 sets of congruent sides- opposite angles congruent- consecutive angles supplementary- diagonals bisect each other- diagonals form 2 congruent triangles

parallelogram: -quadrilateral whose opposite sides are parallel

1. In your notes, use a ruler to create a parallelogram.

2. With your protractor, measure each interior angle of your

parallelogram.

112°

3. What can you say about opposite angles of a parallelogram? Compare your parallelogram other parallelograms around you.

112°

The _______________of a parallelogram are ________.

opposite angles

congruent

What is the measure of A?

127°

What is the measure of B?

53°

consecutive angles - angles that share a side

112°

consecutive angles - one set of consecutive angles

112°

A relationship exists between consecutive angles of a parallelogram. 4. Find the sum of the

measures of each pair of consecutive angles in your parallelogram.

The _______________of a parallelogram are _____________.

consecutive angles

supplimentary

What is the measure of C?

38°

What is the measure of D?

86°

What is the measure of E?

94°

What is the measure of F?

86°

5. Use your compass to compare the measures of opposite sides of a parallelogram.

The _______________of a parallelogram are _____________.

opposite sides

congruent

The perimeter of parallelogram ABCD is 48m.

perimeter = 48m

mAD=?

perimeter = 48m

mAD = 16m

perimeter = 48m

mAB=?

perimeter = 48m

mAB= 8m

perimeter = 48m

mCD= ?

perimeter = 48m

mCD= 8m

6. Construct the two diagonals on your parallelogram. The diagonals intersect each other.

Do the diagonals bisect each other?

YES

Use your compass to check.

The _______________of a parallelogram

_________________.

diagonals

bisect each other

mIN=5 inches

mNH =?

mIN=5 inches

mNH = 5 inches

Properties of Special Parallelograms

Objectives

1. Discover special properties of a rectangle, rhombus, and square.

rhombus

-quadrilateral with four congruent sides

If two parallel lines are intersected by a second pair of parallel lines the same distance apart as the first pair, then the parallelogram formed is a ___________.rhombus

The diagonals of a rhombus are perpendicular bisectors of each other.

states that the diagonals intersect at right angles.

The diagonals of a rhombus bisect the angles of the rhombus.

states that the diagonals bisect each angle of the rhombus so…..

states that the diagonals bisect each angle of the rhombus so…..

rectangle

-equiangular parallelogram

The measure of each angle of a rectangle is ___°.90

rectangle

Each angle of a rectangle has the measure of 90°

The diagonals of a rectangle are ____________.equal length

The diagonals of a rectangle are ____________.equal length

The diagonals of a rectangle are ____________.equal length

square

-equiangular rhombus

-equilateral rectangle