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Special Quadrilaterals 2

May 30, 2018

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Four sided polygon

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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.

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Foldable

2. 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!

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Foldable

4. Write

QUADRILATERALS

down the left hand side

The fold crease

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Foldable

5. Fold over the top cut

section and write

PARALLELOGRAM

on the outside.

The fold crease

6. Reopen the fold.

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Foldable

7. On the left hand

section, draw a

parallelogram.

8. On the right hand

side, list all of the

properties of a

parallelogram.

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Now, Let¶s review what we learnedlast class

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A quadrilateral is a

PARALLELOGRAMif and only if it

has two sets ofparallel sides

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

3. BOTH pairs of opposite angles arecongruent

4.C

onsecutive angles are supplementary

5.diagonals BISECT each other

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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.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

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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.

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A parallelogram withFOUR RIGHT ANGLES

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A quadrilateral is a

RECTANGLE if andonly if it has four

right angles

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Diagonals are Congruent

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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. All properties of parallelogram.

1. Opposite sides parallel.

2. Opposite sides congruent.

3. Opposite angles are congruent.

4. Consecutive angles are supplementary.

5. Diagonals bisect each other.

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Foldable

* On the left hand

section, draw a

rhombus.

* On the right hand

side, list all of theproperties 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.

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A parallelogram with FOURCONGRUENT SIDES

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A quadrilateral is aRHOMBUS if andonly if it has four

congruent sides

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Diagonals Bisect A Pair ofOpposite Angles

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Diagonals are Perpendicular

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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.

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Foldable

* On the left hand

section, draw a square.

* On the right hand

side, list all of theproperties 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.

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A parallelogram with

FOUR RIGHT ANGLES AND FOUR CONGRUENT 

SIDES

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A quadrilateral is aSQUARE if and

only if it has fourcongruent sides

and four rightangles

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Holds same properties as

Rhombus and Rectangle

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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.

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Foldable

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

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ONE PAIR OF PARALLELSIDES

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A quadrilateral is aTRAPEZOID if andonly if it has ONE

pair of parallelsides

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legleg

base

base

Leg angles aresupplementary

Leg angle 1

Leg angle 2

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Base (b2)

Base (b1)

Midsegment is ½ the sum ofthe lengths of the bases

Midsegment=½ (b1 + b2)

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legleg

base

base

Isosceles:Base angles are congruent

Base angle 2Base angle 1

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Isosceles:Diagonals are congruent

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TWO PAIRS OFCONSECUT IVE CONGRUENT 

SIDES (opposite sides not congruent)

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A quadrilateral is aKITE if and only ifit has two pairs of

congruentconsecutive sides

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Diagonals are perpendicular

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Short diagonal is bisected

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ONE pair of opposite anglesare congruent (not both)

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The other angles are bisectedby the diagonal

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Foldable

1. One pair of parallel sides

2. Leg angles supplementary

3. Midsegment= ½(b1 + b2)

4. Isosceles²see 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

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Isosceles Trapezoid:

1. 2 pairs of congruent base

angles

2. Diagonals are congruent

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QUADRILATERALS

PARALLELOGRAMS

RHOMBUSES

RECTANGLES

Squares

E

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QUADRILATERALS

PARALLELOGRAMS

RHOMBUSES

RECTANGLES

Squares

1. Diagonals bisect angles

2. Diag. perpendicular 

3. 4 equal sides

1. Polygon

2. 4 sides

1. 4 rt. angles

2. Diagonals

congruent

5. Consecutive angles supplementary

4. Diagonals Bisect3. Opposite Sides parallel

2. Opposite Angles congruent

1. Opposite Sides congruent

DR L TER L l

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QUADRILATERALS

PARALLELOGRAMS

RHOMBUSES

RECTANGLES

Squares

1. Diagonals bisect angles

2. Diag. perpendicular 

3. 4 equal sides

1. Polygon

2. 4 sides

1. 4 rt. angles

2. Diagonals

congruent

5. Consecutive angles supplementary

4. Diagonals Bisect3. Opposite Sides parallel

2. Opposite Angles congruent

1. Opposite Sides congruent

Trapezoids

Kites