Special

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Special Quadrilaterals
Sect 5.10, 5.11, 5.12
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Quadrilateral
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
The fold crease
2. Now, divide the right hand section into 5
sections by drawing 4 evenly spaced lines.
3. Use scissors to cut along your drawn line, but
ONLY to the crease!
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Foldable
The fold crease
4. Write QUADRILATERALS down the left hand side
QUADRILATERALS
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Foldable
The fold crease
5. Fold over the top cut section and write
PARALLELOGRAM on the outside.
Parallelogram
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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Parallelograms
Now, Lets review what we learned last class
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A quadrilateral is a PARALLELOGRAM if and only if
it has two sets of parallel sides
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Properties
1.BOTH pairs of opposite sides are parallel
2.BOTH pairs of opposite sides are congruent
3. BOTH pairs of opposite angles are congruent
4.Consecutive 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.
1. Opposite sides parallel. 2. Opposite sides
congruent. 3. Opposite angles are congruent. 4.
Consecutive angles are supplementary. 5.
Diagonals bisect each other.
RECTANGLE
Reopen the fold.
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Foldable
On the left hand section, draw 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.
On the right hand side, list all of the
properties of a rectangle.
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RECTANGLE
A parallelogram with FOUR RIGHT ANGLES
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A quadrilateral is a RECTANGLE if and only if it
has four right angles
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RECTANGLE
Diagonals are Congruent
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Foldable
Fold over the third cut section and write
RHOMBUS on the outside.
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.
Reopen the fold.
RHOMBUS
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Foldable
On the left hand section, draw 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.
On the right hand side, list all of the
properties of a rhombus.
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RHOMBUS
A parallelogram with FOUR CONGRUENT SIDES
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A quadrilateral is a RHOMBUS if and only if it
has four congruent sides
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RHOMBUS
Diagonals Bisect A Pair of Opposite Angles
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RHOMBUS
Diagonals are Perpendicular
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Foldable
Fold over the fourth cut section and write
SQUARE on the outside.
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.
Reopen the fold.
1. Has 4 Congruent sides 2. Diagonals bisect
opposite angles. 3. Diagonals are
perpendicular. 4. All properties of
parallelograms.
SQUARE
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Foldable
On the left hand section, draw 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.
On the right hand side, list all of the
properties of a square.
1. Has 4 Congruent sides 2. Diagonals bisect
opposite angles. 3. Diagonals are
perpendicular. 4. All properties of
parallelograms.
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SQUARE
A parallelogram with FOUR RIGHT ANGLES AND FOUR
CONGRUENT SIDES
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A quadrilateral is a SQUARE if and only if it has
four congruent sides and four right angles
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SQUARE
Holds same properties as Rhombus and Rectangle
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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
TRAPEZOID KITE
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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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Trapezoid
ONE PAIR OF PARALLEL SIDES
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A quadrilateral is a TRAPEZOID if and only if it
has ONE pair of parallel sides
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Trapezoid
Leg angle 1
Leg angle 2
Leg angles are supplementary
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Trapezoid
Midsegment ½ (b1 b2)
Midsegment is ½ the sum of the lengths of the
bases
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Trapezoid
Base angle 2
Base angle 1
Isosceles Base angles are
congruent
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Trapezoid
Isosceles Diagonals are congruent
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KITE
TWO PAIRS OF CONSECUTIVE CONGRUENT SIDES
(opposite sides not congruent)
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A quadrilateral is a KITE if and only if it has
two pairs of congruent consecutive sides
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KITE
Diagonals are perpendicular
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KITE
Short diagonal is bisected
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KITE
ONE pair of opposite angles are congruent (not
both)
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KITE
The other angles are bisected by the diagonal
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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.
QUADRILATERALS
1. 4 congruent sides and 4 congruent
(right) angles 2. All properties of
parallelogram, rectangle, and rhombus
1. One pair of parallel sides 2. Leg angles
supplementary 3. Midsegment ½(b1 b2) 4.
Isoscelessee 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
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Isosceles Trapezoid 1. 2 pairs of congruent
base angles 2. Diagonals are congruent
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Let's make a Venn Diagram Relating all of the
Properities of our quadrilaterals
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QUADRILATERALS
PARALLELOGRAMS
RHOMBUSES
RECTANGLES
Squares
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QUADRILATERALS
1. Polygon
2. 4 sides
PARALLELOGRAMS
1. Opposite Sides congruent
RHOMBUSES
1. Diagonals bisect angles
RECTANGLES
2. Diag. perpendicular
Squares
1. 4 rt. angles
3. 4 equal sides
2. Diagonals congruent
2. Opposite Angles congruent
4. Diagonals Bisect
3. Opposite Sides parallel
5. Consecutive angles supplementary
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QUADRILATERALS
1. Polygon
Trapezoids
2. 4 sides
PARALLELOGRAMS
1. Opposite Sides congruent
RHOMBUSES
1. Diagonals bisect angles
RECTANGLES
2. Diag. perpendicular
Squares
1. 4 rt. angles
3. 4 equal sides
2. Diagonals congruent
2. Opposite Angles congruent
4. Diagonals Bisect
3. Opposite Sides parallel
Kites
5. Consecutive angles supplementary