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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)
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!
Lesson 6-1: Quadrilaterals
VocabQuadrilateralOppositeConsecutive
• 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
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
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!
Quadrilateral RelationshipsQuadrilaterals
Parallelograms
Rectangles RhombiSquares
Trapezoids
Kites
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
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)
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
Properties of Quadrilaterals
• Review handout
Foldable
1. Take out a piece of notebook paper fold the right edge over to the pink line.
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!
Foldable4. Write PARALLELOGRAMS down the left hand side
The fold crease
Foldable5. Fold over the top cut section and write PARALLELOGRAM on the outside.
The fold crease
6. Reopen the fold.
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.
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
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
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.
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.
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
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
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
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?
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
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
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)
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
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
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
Kite• Properties
– 2 pairs of consecutive (adjacent) sides__________
– 1 diagonal is ___________
– Diagonals are _________________
– 1 diagonal is an _________________
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
Kite• Properties
– 2 pairs of consecutive (adjacent) sides – 1 diagonal is– Diagonals are– 1 diagonal is an
congruent
bisected
perpendicular (900)
angle bisector
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)
