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Transcript of * Quadrilateral I have exactly four sides. *Trapezoid I have only one set of parallel sides. [The...
![Page 1: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/1.jpg)
*Quadrilateral
I have exactly four sides.
![Page 2: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/2.jpg)
*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.]
![Page 3: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/3.jpg)
![Page 4: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/4.jpg)
Isosceles TrapezoidI have:- only one set of parallel sides- base angles congruent- legs congruent- diagonals congruent- opposite angles supplementary
![Page 5: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/5.jpg)
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
![Page 6: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/6.jpg)
![Page 7: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/7.jpg)
TRAPEZOIDS-quadrilateral with one pair of parallel sides
![Page 8: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/8.jpg)
TRAPEZOIDS
-parallel sidesbases
![Page 9: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/9.jpg)
TRAPEZOIDS
-pair of angles that share a basebase angles
![Page 10: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/10.jpg)
TRAPEZOIDS
-pair of angles that share a basebase angles
![Page 11: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/11.jpg)
Open books to page 291. Work on investigation 6.3.2 on your own.
![Page 12: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/12.jpg)
Trapezoid Consecutive Angles Conjecture
The consecutive angles between the bases of a trapezoid are ______________. supplementary
![Page 13: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/13.jpg)
TRAPEZOIDSm1 + m2 =180°
m3 + m4 =180°
![Page 14: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/14.jpg)
TRAPEZOIDS
-two nonparallel sides are congruent
isosceles trapezoid
![Page 15: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/15.jpg)
Isosceles Trapezoid Conjecture
The base angles of an isosceles trapezoid are ______________. congruent
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TRAPEZOIDSm1 = m4
m2 = m3
![Page 17: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/17.jpg)
Isosceles Trapezoid Diagonals Conjecture
The diagonals of an isosceles trapezoid are ______________.
congruent
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TRAPEZOIDSmAC = mBD
![Page 19: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/19.jpg)
Properties of Parallelograms
Objectives:
1. Discover properties of parallelograms.
![Page 20: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/20.jpg)
parallelogram: -quadrilateral whose opposite sides are parallel
![Page 21: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/21.jpg)
![Page 22: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/22.jpg)
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
![Page 23: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/23.jpg)
![Page 24: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/24.jpg)
parallelogram: -quadrilateral whose opposite sides are parallel
![Page 25: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/25.jpg)
1. In your notes, use a ruler to create a parallelogram.
![Page 26: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/26.jpg)
2. With your protractor, measure each interior angle of your
parallelogram.
112°
![Page 27: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/27.jpg)
3. What can you say about opposite angles of a parallelogram? Compare your parallelogram other parallelograms around you.
112°
![Page 28: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/28.jpg)
The _______________of a parallelogram are ________.
opposite angles
congruent
![Page 29: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/29.jpg)
What is the measure of A?
127°
![Page 30: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/30.jpg)
What is the measure of B?
53°
![Page 31: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/31.jpg)
consecutive angles - angles that share a side
112°
![Page 32: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/32.jpg)
consecutive angles - one set of consecutive angles
112°
![Page 33: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/33.jpg)
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.
![Page 34: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/34.jpg)
The _______________of a parallelogram are _____________.
consecutive angles
supplimentary
![Page 35: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/35.jpg)
What is the measure of C?
38°
![Page 36: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/36.jpg)
What is the measure of D?
86°
![Page 37: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/37.jpg)
What is the measure of E?
94°
![Page 38: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/38.jpg)
What is the measure of F?
86°
![Page 39: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/39.jpg)
5. Use your compass to compare the measures of opposite sides of a parallelogram.
![Page 40: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/40.jpg)
The _______________of a parallelogram are _____________.
opposite sides
congruent
![Page 41: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/41.jpg)
The perimeter of parallelogram ABCD is 48m.
![Page 42: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/42.jpg)
perimeter = 48m
mAD=?
![Page 43: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/43.jpg)
perimeter = 48m
mAD = 16m
![Page 44: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/44.jpg)
perimeter = 48m
mAB=?
![Page 45: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/45.jpg)
perimeter = 48m
mAB= 8m
![Page 46: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/46.jpg)
perimeter = 48m
mCD= ?
![Page 47: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/47.jpg)
perimeter = 48m
mCD= 8m
![Page 48: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/48.jpg)
6. Construct the two diagonals on your parallelogram. The diagonals intersect each other.
![Page 49: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/49.jpg)
Do the diagonals bisect each other?
YES
Use your compass to check.
![Page 50: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/50.jpg)
The _______________of a parallelogram
_________________.
diagonals
bisect each other
![Page 51: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/51.jpg)
mIN=5 inches
mNH =?
![Page 52: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/52.jpg)
mIN=5 inches
mNH = 5 inches
![Page 53: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/53.jpg)
Properties of Special Parallelograms
Objectives
1. Discover special properties of a rectangle, rhombus, and square.
![Page 54: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/54.jpg)
![Page 55: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/55.jpg)
rhombus
-quadrilateral with four congruent sides
![Page 56: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/56.jpg)
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
![Page 57: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/57.jpg)
The diagonals of a rhombus are perpendicular bisectors of each other.
![Page 58: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/58.jpg)
states that the diagonals intersect at right angles.
![Page 59: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/59.jpg)
The diagonals of a rhombus bisect the angles of the rhombus.
![Page 60: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/60.jpg)
states that the diagonals bisect each angle of the rhombus so…..
![Page 61: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/61.jpg)
states that the diagonals bisect each angle of the rhombus so…..
![Page 62: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/62.jpg)
![Page 63: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/63.jpg)
rectangle
-equiangular parallelogram
![Page 64: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/64.jpg)
The measure of each angle of a rectangle is ___°.90
![Page 65: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/65.jpg)
rectangle
Each angle of a rectangle has the measure of 90°
![Page 66: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/66.jpg)
The diagonals of a rectangle are ____________.equal length
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The diagonals of a rectangle are ____________.equal length
![Page 68: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/68.jpg)
The diagonals of a rectangle are ____________.equal length
![Page 69: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/69.jpg)
![Page 70: * 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.](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649ea95503460f94bae09e/html5/thumbnails/70.jpg)
square
-equiangular rhombus
-equilateral rectangle