* 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