Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6,...
-
Upload
mark-merritt -
Category
Documents
-
view
218 -
download
0
Transcript of Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6,...
![Page 1: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/1.jpg)
Warmup 6-1
On a half piece of paper find the midpoint, distance, and slope for each.
1) (2, 5), (6, 17)
2) (-2, 3), (4, 6)
3) (7, -3), (4, 10)
![Page 2: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/2.jpg)
Skills…answers
1) Midpoint (4, 11) Distance = 12.6 Slope = 3
2) Midpoint (1, 4.5) Distance = 6.7
Slope = ½
3) Midpoint (5.5, 3.5) Distance = 13.3 Slope = -4.3 (-13/3)
We will have a 5 pointquiz every day forthis chapter on this
material!
![Page 3: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/3.jpg)
Lesson 6-1: Quadrilaterals
VocabQuadrilateralOppositeConsecutive
![Page 4: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/4.jpg)
• Quadrilateral → any 4-sided figure
• Opposite– Opposite sides → do not touch– Opposite angles → diagonal to each other
• Consecutive (Adjacent)– Consecutive sides → touch– Consecutive angles → share a side
![Page 5: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/5.jpg)
A
B
C
D
1
2
43
Name opposite and consecutive sides and angles.
Opposite sides:
Consecutive sides:
Opposite angles:
Consecutive angles:
AB & CD; BC & AD
AB & BC; AB & AD; CD & BC; CD & AD
Angles 1 & 4; and 2 & 3
Angles 1 & 2; 1 & 3; 2 & 4; 3 & 4
![Page 6: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/6.jpg)
Types of Quadrilaterals
2 pairs of parallel, opposite sides 1 pair of parallel,
opposite sides
No parallel sides
Quadrilateral
Parallelogram
Rectangle
Square
Trapezoid Kite
Rhombus
Each shape will have any properties of shape above
it!
![Page 7: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/7.jpg)
Quadrilateral RelationshipsQuadrilaterals
Parallelograms
Rectangles RhombiSquares
Trapezoids
Kites
![Page 8: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/8.jpg)
6-1 Problems
• Determine the figure by looks
• Determine the figure by calculations– Find length of opposite sides → distance formula– Find slope of opposite sides → slope formula
• Find the missing value– Set opposite sides equal → solve– Consecutive angles add to 1800 → solve
![Page 9: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/9.jpg)
Midpoint, Distance, Slope Quiz 1
On a piece of paper find the midpoint, distance, and slope for each.
1) (-1, 3), (0, 5)
2) (4, -2), (8, -5)
3) (3, 5), (6, 14)
![Page 10: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/10.jpg)
Quiz 1…answers
1) Midpoint (-0.5, 4) Distance = 2.2 Slope = 2
2) Midpoint (6, -3.5) Distance = 5 Slope = -3/4 or -0.75
3) Midpoint (4.5, 9.5) Distance = 9.5 Slope = 3
![Page 11: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/11.jpg)
Properties of Quadrilaterals
• Review handout
![Page 12: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/12.jpg)
Foldable
1. Take out a piece of notebook paper fold the right edge over to the pink line.
![Page 13: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/13.jpg)
Foldable2. Now, divide the right hand section into 4 sections by drawing 3 evenly spaced lines.
The fold crease
3. Use scissors to cut along your drawn line, but ONLY to the crease!
![Page 14: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/14.jpg)
Foldable4. Write PARALLELOGRAMS down the left hand side
The fold crease
![Page 15: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/15.jpg)
Foldable5. Fold over the top cut section and write PARALLELOGRAM on the outside.
The fold crease
6. Reopen the fold.
![Page 16: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/16.jpg)
Foldable7. On the left hand section, draw a parallelogram.
1. Opposite sides parallel
2. Opposite sides congruent
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Consecutive angles are supplementary
8. On the right hand side, list all of the properties of a parallelogram.
9. Place in your notebook and save for tomorrow.
![Page 17: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/17.jpg)
Foldable* Fold over the second cut section and write RECTANGLE on the outside.
* Reopen the fold.
1. Opposite sides parallel
2. Opposite sides congruent
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Consecutive angles are supplementary
![Page 18: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/18.jpg)
Foldable* On the left hand section, draw a rectangle.
* On the right hand side, list all of the properties of a rectangle.
1. Properties of a parallelogram.
2. Has a right angle
3. Diagonals are congruent.
1. Opposite sides parallel
2. Opposite sides congruent
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Consecutive angles are supplementary
![Page 19: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/19.jpg)
Foldable* Fold over the third cut section and write RHOMBUS on the outside.
* Reopen the fold.
1. Opposite sides parallel
2. Opposite sides congruent
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Consecutive angles are supplementary
1. Properties of a parallelogram.
2. Has a right angle
3. Diagonals are congruent.
![Page 20: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/20.jpg)
Foldable* On the left hand section, draw a rhombus.
* On the right hand side, list all of the properties of a rhombus. 1. Properties of a parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
1. Opposite sides parallel
2. Opposite sides congruent
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Consecutive angles are supplementary
1. Properties of a parallelogram.
2. Has a right angle
3. Diagonals are congruent.
![Page 21: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/21.jpg)
Foldable* Fold over the third cut section and write SQUARE on the outside.
* Reopen the fold.
1. Opposite sides parallel
2. Opposite sides congruent
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Consecutive angles are supplementary
1. Properties of a parallelogram.
2. Has a right angle
3. Diagonals are congruent.
1. Properties of a parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
![Page 22: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/22.jpg)
Foldable* On the left hand section, draw a square.
* On the right hand side, list all of the properties of a square.
1. Is a parallelogram, rectangle, and rhombus
2. 4 congruent sides and 4 congruent (right) angles
1. Opposite sides parallel
2. Opposite sides congruent
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Consecutive angles are supplementary
1. Properties of a parallelogram.
2. Has a right angle
3. Diagonals are congruent.
1. Properties of a parallelogram
2. Has 4 Congruent sides
3. Diagonals are perpendicular.
4. Diagonals bisect opposite angles
![Page 23: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/23.jpg)
Lesson 6-2/6-3: Parallelograms(Put on back of foldable)
• Proving a parallelogram– 2 pairs of opposite sides congruent– 1 pair of opposite sides congruent & parallel– Diagonals bisect each other– 2 pairs of opposite angles congruent
![Page 24: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/24.jpg)
Using Alternate Interior Angles
• If you have a parallelogram, then any diagonal is a _______________
• ______________________ are created by the diagonal like angles ____ and ____
• THESE ANGLES _______________________
Remember this diagram?
![Page 25: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/25.jpg)
Using Alternate Interior Angles
• If you have a parallelogram, then any diagonal is a
• are created by the diagonal like angles and
• THESE ANGLES
Remember this diagram?
1
2
transversal
Alternate interior angles1 2
MUST BE CONGRUENT
![Page 26: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/26.jpg)
6-2/6-3 Problems
• Apply properties of parallelograms– Set opposite sides equal to each other– Set parts of diagonal equal to each other– Set opposite angles equal to each other– Consecutive angles add to 1800
![Page 27: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/27.jpg)
Midpoint, Distance, Slope Quiz 2
On a piece of paper find the midpoint, distance, and slope for each.
1) (4, -2), (0, 3)
2) (12, 15), (20, 2)
3) (10, 5), (10, 16)
![Page 28: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/28.jpg)
Quiz 2…answers
1) Midpoint (2, 0.5) Distance = 6.4 Slope = -5/4 or -1.25
2) Midpoint (16, 8.5) Distance = 15.3 Slope = -13/8 or -1.625
3) Midpoint (10, 10.5) Distance = 11 Slope = 0
![Page 29: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/29.jpg)
6-4 Special Parallelograms
• Apply properties of rectangles, rhombi, and squares
• Know diagonal properties– Diagonals bisect each other → all– Diagonals equal → rectangle & square– Diagonals perpendicular → rhombus & square– Diagonals bisect angles → rhombus & square
• Area of a rhombus:
21hom 2
1ddA busr
![Page 30: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/30.jpg)
Trapezoids• Trapezoid Properties
– 1 pair of _______________– 2 pairs of consecutive (adjacent) angles are ___________
→ pairs that touch the same ______
• ____________ Trapezoid– All properties of a__________– Legs are __________– Base angles (angles touching the same base) are ________– Diagonals are___________
• __________ Trapezoid– All properties of a____________– Has a ________ angle
![Page 31: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/31.jpg)
Kite• Properties
– 2 pairs of consecutive (adjacent) sides__________
– 1 diagonal is ___________
– Diagonals are _________________
– 1 diagonal is an _________________
![Page 32: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/32.jpg)
Trapezoids• Trapezoid Properties
– 1 pair of – 2 pairs of consecutive (adjacent) angles are
→ pairs that touch the same
• Trapezoid– All properties of a – Legs are – Base angles (angles touching the same base) are – Diagonals are
• Trapezoid– All properties of a – Has a angle
parallel sidessupplementary
legs
Isoscelestrapezoid
congruentcongruent
congruent
Righttrapezoid
right
600
1200
![Page 33: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/33.jpg)
Kite• Properties
– 2 pairs of consecutive (adjacent) sides – 1 diagonal is– Diagonals are– 1 diagonal is an
congruent
bisected
perpendicular (900)
angle bisector
![Page 34: Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. 1)(2, 5), (6, 17) 2)(-2, 3), (4, 6) 3)(7, -3), (4, 10)](https://reader033.fdocuments.us/reader033/viewer/2022051215/56649ea05503460f94ba38a9/html5/thumbnails/34.jpg)
6-5 Problems
• Know the properties of trapezoids & kites
• Use angle relationships– Trapezoids: angles between parallel sides are
supplementary (add to 1800)– Kites: diagonals are perpendicular (900)