* Quadrilateral I have exactly four sides.

*Trapezoid I 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 Trapezoid I have: - only one set of parallel sides - base angles congruent - legs congruent - diagonals congruent - opposite angles supplementary

Parallelogram I 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 sides bases

TRAPEZOIDS -pair of angles that share a base base angles

TRAPEZOIDS -pair of angles that share a base base angles

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

Trapezoid Consecutive Angles Conjecture The consecutive angles between the bases of a trapezoid are ______________. supplementary

TRAPEZOIDS m  1 + m  2 =180° m  3 + m  4 =180°

TRAPEZOIDS -two nonparallel sides are congruent isosceles trapezoid

Isosceles Trapezoid Conjecture The base angles of an isosceles trapezoid are ______________. congruent

TRAPEZOIDS m  1 = m  4 m  2 = m  3

Isosceles Trapezoid Diagonals Conjecture The diagonals of an isosceles trapezoid are ______________. congruent

TRAPEZOIDS mAC = mBD

Properties of Parallelograms Objectives: 1. Discover properties of parallelograms.

parallelogram: -quadrilateral whose opposite sides are parallel

Parallelogram I 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 °

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

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…..

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

equal length

The diagonals of a rectangle are ____________. equal length

square -equiangular rhombus -equilateral rectangle