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