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Warmup 6-1 On a half piece of paper find the midpoint, distance, and slope for each. (2, 5), (6, 17) (-2, 3), (4, 6) (7, -3), (4, 10)

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**Skills…answers Midpoint (4, 11) Midpoint (1, 4.5) Midpoint (5.5, 3.5)**

Distance = 12.6 Slope = 3 Midpoint (1, 4.5) Distance = 6.7 Slope = ½ Midpoint (5.5, 3.5) Distance = 13.3 Slope = -4.3 (-13/3) We will have a 5 point quiz every day for this chapter on this material!

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**Lesson 6-1: Quadrilaterals**

Vocab Quadrilateral Opposite Consecutive

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**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

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**Name opposite and consecutive sides and angles.**

B 2 A 1 3 D 4 C Opposite sides: AB & CD; BC & AD Consecutive sides: AB & BC; AB & AD; CD & BC; CD & AD Opposite angles: Angles 1 & 4; and 2 & 3 Consecutive angles: Angles 1 & 2; 1 & 3; 2 & 4; 3 & 4

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**Quadrilateral Parallelogram Kite Trapezoid Rectangle Rhombus Square**

Types of Quadrilaterals Quadrilateral 2 pairs of parallel, opposite sides No parallel sides 1 pair of parallel, opposite sides Parallelogram Kite Trapezoid Rectangle Rhombus Each shape will have any properties of shape above it! Square

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**Quadrilateral Relationships**

Quadrilaterals Parallelograms Trapezoids Rectangles Rhombi Squares Kites

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**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

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**Midpoint, Distance, Slope Quiz 1**

On a piece of paper find the midpoint, distance, and slope for each. (-1, 3), (0, 5) (4, -2), (8, -5) (3, 5), (6, 14)

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**Quiz 1…answers Midpoint (-0.5, 4) Midpoint (6, -3.5)**

Distance = 2.2 Slope = 2 Midpoint (6, -3.5) Distance = 5 Slope = -3/4 or -0.75 Midpoint (4.5, 9.5) Distance = 9.5 Slope = 3

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**Properties of Quadrilaterals**

Review handout

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Foldable 1. Take out a piece of notebook paper fold the right edge over to the pink line.

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**Foldable The fold crease**

2. Now, divide the right hand section into 4 sections by drawing 3 evenly spaced lines. 3. Use scissors to cut along your drawn line, but ONLY to the crease!

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**Foldable ParallelOgrams The fold crease**

4. Write PARALLELOGRAMS down the left hand side ParallelOgrams

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**Foldable Parallelogram Parallelograms The fold crease**

5. Fold over the top cut section and write PARALLELOGRAM on the outside. Parallelogram 6. Reopen the fold. Parallelograms

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**Foldable Parallelograms**

7. 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. Parallelograms 9. Place in your notebook and save for tomorrow.

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**Foldable Parallelograms RECTANGLE**

* Fold over the second cut section and write RECTANGLE on the outside. 1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary * Reopen the fold. RECTANGLE Parallelograms

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**Foldable Parallelograms * On the left hand section, draw a rectangle.**

1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary * 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. Parallelograms

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**Foldable Parallelograms RHOMBUS**

* Fold over the third cut section and write RHOMBUS on the outside. 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. * Reopen the fold. Parallelograms RHOMBUS

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**Foldable Parallelogram * On the left hand section, draw a rhombus.**

1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary * On the right hand side, list all of the properties of a rhombus. 1. Properties of a parallelogram. 2. Has a right angle 3. Diagonals are congruent. Parallelogram 1. Properties of a parallelogram 2. Has 4 Congruent sides 3. Diagonals are perpendicular. 4. Diagonals bisect opposite angles

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**Foldable Parallelograms SQUARE**

* Fold over the third cut section and write SQUARE on the outside. 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. * Reopen the fold. Parallelograms 1. Properties of a parallelogram 2. Has 4 Congruent sides 3. Diagonals are perpendicular. 4. Diagonals bisect opposite angles SQUARE

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**Foldable Parallelograms * On the left hand section, draw a square.**

1. Opposite sides parallel 2. Opposite sides congruent 3. Diagonals bisect each other 4. Opposite angles are congruent 5. Consecutive angles are supplementary * On the right hand side, list all of the properties of a square. 1. Properties of a parallelogram. 2. Has a right angle 3. Diagonals are congruent. Parallelograms 1. Properties of a parallelogram 2. Has 4 Congruent sides 3. Diagonals are perpendicular. 4. Diagonals bisect opposite angles 1. Is a parallelogram, rectangle, and rhombus 2. 4 congruent sides and 4 congruent (right) angles

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**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

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**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?

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**Using Alternate Interior Angles**

If you have a parallelogram, then any diagonal is a are created by the diagonal like angles and THESE ANGLES transversal Remember this diagram? 1 2 Alternate interior angles 1 2 MUST BE CONGRUENT

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**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

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**Midpoint, Distance, Slope Quiz 2**

On a piece of paper find the midpoint, distance, and slope for each. (4, -2), (0, 3) (12, 15), (20, 2) (10, 5), (10, 16)

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**Quiz 2…answers Midpoint (2, 0.5) Midpoint (16, 8.5)**

Distance = 6.4 Slope = -5/4 or -1.25 Midpoint (16, 8.5) Distance = 15.3 Slope = -13/8 or Midpoint (10, 10.5) Distance = 11 Slope = 0

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**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:

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**Trapezoids Trapezoid Properties ____________ Trapezoid**

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

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**Kite Properties 2 pairs of consecutive (adjacent) sides__________**

1 diagonal is ___________ Diagonals are _________________ 1 diagonal is an _________________

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**Trapezoids Trapezoid Properties Trapezoid Isosceles Right 1 pair of**

1200 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 Has a angle parallel sides 600 supplementary legs Isosceles trapezoid congruent congruent congruent Right trapezoid right

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**Kite Properties 2 pairs of consecutive (adjacent) sides 1 diagonal is**

Diagonals are 1 diagonal is an congruent bisected perpendicular (900) angle bisector

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**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)

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