Quadrilateral Four sided polygon.
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Transcript of Quadrilateral Four sided polygon.
![Page 1: Quadrilateral Four sided polygon.](https://reader035.fdocuments.in/reader035/viewer/2022082202/5a4d1b1a7f8b9ab059993208/html5/thumbnails/1.jpg)
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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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!
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Foldable4. Write QUADRILATERALS down the left hand side
The fold crease
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Foldable5. Fold over the top cut section and write PARALLELOGRAM on the outside.
The fold crease
6. Reopen the fold.
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Foldable7. 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 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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1.BOTH pairs of opposite sides are parallel2.BOTH pairs of opposite sides are congruent3. BOTH pairs of opposite angles are congruent4.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.
* 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 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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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 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.
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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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Diagonals Bisect A Pair of Opposite 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 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.
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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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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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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
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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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leg leg
base
base
Leg angles are supplementary
Leg angle 1
Leg angle 2
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Base (b2)
Base (b1)
Midsegment is ½ the sum of the lengths of
the bases
Midsegment =½ (b1
+ b2)
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leg leg
base
base
Isosceles: Base angles are congruent
Base angle 2
Base angle 1
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Isosceles: Diagonals are congruent
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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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Diagonals are perpendicular
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Short diagonal is bisected
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ONE pair of opposite angles are congruent (not
both)
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The other angles are bisected by the diagonal
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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 congruent2. 1 pair of opposite angles congruent3. Diagonals perpendicular4. Small diagonal bisected5. 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
RECTANGLESSquares
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QUADRILATERALSPARALLELOGRAMS
RHOMBUSES
RECTANGLESSquares
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
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QUADRILATERALSPARALLELOGRAMS
RHOMBUSES
RECTANGLESSquares
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