TechMathI - 5.3 - Properties of Quadrilaterals

32

Transcript of TechMathI - 5.3 - Properties of Quadrilaterals

Page 1: TechMathI - 5.3 - Properties of Quadrilaterals
Page 2: TechMathI - 5.3 - Properties of Quadrilaterals

Four sided polygon

Page 3: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line.

Page 4: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable2. Now, divide the right hand section into 5 sections by drawing 4 evenly spaced lines.

The fold crease

3. Use scissors to cut along your drawn line, but ONLY to the crease!

Page 5: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable4. Write QUADRILATERALS down the left hand side

The fold crease

Page 6: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable5. Fold over the top cut section and write PARALLELOGRAM on the outside.

The fold crease

6. Reopen the fold.

Page 7: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable7. On the left hand section, draw a parallelogram.

8. On the right hand side, list all of the properties of a parallelogram.

Page 8: TechMathI - 5.3 - Properties of Quadrilaterals
Page 9: TechMathI - 5.3 - Properties of Quadrilaterals

A quadrilateral is a

PARALLELOGRAM if and only if it has two sets

of parallel sides

Page 10: TechMathI - 5.3 - Properties of Quadrilaterals

1.BOTH pairs of opposite sides are parallel2.BOTH pairs of opposite sides are congruent

3. BOTH pairs of opposite angles are congruent

Page 11: TechMathI - 5.3 - Properties of Quadrilaterals

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. Opposite angles are congruent.

Page 12: TechMathI - 5.3 - Properties of Quadrilaterals

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

* On the right hand side, list all of the properties of a rectangle.

1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

Page 13: TechMathI - 5.3 - Properties of Quadrilaterals

1. A parallelogram with FOUR RIGHT

ANGLES

Page 14: TechMathI - 5.3 - Properties of Quadrilaterals

2. Diagonals are congruent

3. Opposite sides congruent.

Page 15: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable* Fold over the third cut section and write RHOMBUS on the outside.

* Reopen the fold.

1. Has 4 right angles.

2. Diagonals are congruent.

3. Opposite sides congruent.

1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

Page 16: TechMathI - 5.3 - Properties of Quadrilaterals

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

* On the right hand side, list all of the properties of a rhombus.

1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

1. Has 4 right angles.

2. Diagonals are congruent.

3. All properties of parallelogram.

Page 17: TechMathI - 5.3 - Properties of Quadrilaterals

1. A parallelogram with FOUR CONGRUENT SIDES

Page 18: TechMathI - 5.3 - Properties of Quadrilaterals

2. Diagonals Bisect Opposite Angles

Page 19: TechMathI - 5.3 - Properties of Quadrilaterals

3. Diagonals are Perpendicular

Page 20: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable* Fold over the fourth cut section and write SQUARE on the outside.

* Reopen the fold.1. Has 4 Congruent sides

2. Diagonals bisect opposite angles.

3. Diagonals are perpendicular.

4. All properties of parallelograms.

1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

1. Has 4 right angles.

2. Diagonals are congruent.

3. All properties of parallelogram.

Page 21: TechMathI - 5.3 - Properties of Quadrilaterals

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

* On the right hand side, list all of the properties of a square.

1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

1. Has 4 right angles.

2. Diagonals are congruent.

3. All properties of parallelogram.

1. Has 4 Congruent sides

2. Diagonals bisect opposite angles.

3. Diagonals are perpendicular.

4. All properties of parallelograms.

Page 22: TechMathI - 5.3 - Properties of Quadrilaterals

1. A parallelogram with FOUR RIGHT

ANGLES AND FOUR CONGRUENT SIDES

Page 23: TechMathI - 5.3 - Properties of Quadrilaterals

Holds same properties as Rhombus and

Rectangle

Page 24: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable

1. 4 congruent sides and 4 congruent

(right) angles

2. All properties of parallelogram,

rectangle, and rhombus

1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

1. Has 4 right angles.

2. Diagonals are congruent.

3. All properties of parallelogram.

1. Has 4 Congruent sides

2. Diagonals bisect opposite angles.

3. Diagonals are perpendicular.

4. All properties of parallelograms.

Page 25: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

1. Has 4 right angles.

2. Diagonals are congruent.

3. All properties of parallelogram.

1. Has 4 Congruent sides

2. Diagonals bisect opposite angles.

3. Diagonals are perpendicular.

4. All properties of parallelograms.

1. 4 congruent sides and 4 congruent

(right) angles

2. All properties of parallelogram,

rectangle, and rhombus

Page 26: TechMathI - 5.3 - Properties of Quadrilaterals

1. ONE PAIR OF PARALLEL SIDES

Page 27: TechMathI - 5.3 - Properties of Quadrilaterals

leg leg

base

base

2. Leg angles are supplementary

Leg angle 1

Leg angle 2

Page 28: TechMathI - 5.3 - Properties of Quadrilaterals

leg leg

base

base

3. Isosceles: Base angles are

congruent

Base angle 2

Base angle 1

Page 29: TechMathI - 5.3 - Properties of Quadrilaterals

Foldable

1. One pair of parallel sides

2. Leg angles supplementary

3. Midsegment= ½(b1 + b2)

4. Isosceles—see back

1. 2 pairs of consecutive sides congruent

2. 1 pair of opposite angles congruent

3. Diagonals perpendicular

4. Small diagonal bisected

5. Non-congruent angles are bisected

1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

1. Has 4 right angles.

2. Diagonals are congruent.

3. All properties of parallelogram.

1. Has 4 Congruent sides

2. Diagonals bisect opposite angles.

3. Diagonals are perpendicular.

4. All properties of parallelograms.

1. 4 congruent sides and 4 congruent

(right) angles

2. All properties of parallelogram,

rectangle, and rhombus

Page 30: TechMathI - 5.3 - Properties of Quadrilaterals

Name the sides adjacent to MN.

Name the angle opposite <N.

If MN || OP and NO || MP then MNOP is a _____ .

M

N

OP

If NO || MP are the only pair of parallel segments then MNOP is a __________ .

Page 31: TechMathI - 5.3 - Properties of Quadrilaterals

x

2x

Solve for x.

Page 32: TechMathI - 5.3 - Properties of Quadrilaterals

78

92

x

42

Solve for x.