Polygons

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What is a Polygon????

Any ideas?

Write down what you think it is for #1.

A polygon is a closed plane figure with 3 or more sides (all straight lines, no curves).

Classifying Polygons by # of Sides

3 sided Polygon =

Triangle

Hint: Think “Tri”cycle, “tri”pod, “Tri”lateration (Tri means 3)

Classifying Polygons by # of Sides

4 sided Polygon =

Quadrilateral

Hint: Think “Quad”rant, “Quad”ruple, “Quad” (AKA 4-Wheeler)

Classifying Polygons by # of Sides

5 sided Polygon =

Pentagon

Hint: Think “Pent”athalon, or the government building “The Pentagon”

Classifying Polygons by # of Sides

6 sided Polygon =

Hexagon

Hint: Both “Hexagon” and “Six” have an ‘x’ in them

Classifying Polygons by # of Sides

7 sided Polygon =

Heptagon

Hint: ???

Classifying Polygons by # of Sides

8 sided Polygon =

Octagon

Hint: “oct”opus – 8 legs

Classifying Polygons by # of Sides

9 sided Polygon =

Nonagon

Hint: “Non” is similar to “Nine”

Classifying Polygons by # of Sides

10 sided Polygon =

Decagon

Hint: Think “Dec”ade (10 years

Classifying Polygons by # of Sides

11 sided Polygon =

Hendecagon

Hint: ???

Classifying Polygons by # of Sides

12 sided Polygon =

Dodecagon

Hint: ???

Classifying Polygons by # of Sides

Q: What do we call a polygon with more than 12 sides?

A: An ‘n’-gon where ‘n’ is the number of sides

Ex: a 20 sided polygon is a 20-gon

6.2 Properties of Parallelograms

• A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

• In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

Theorem 6.3

• If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Consecutive Angles

• Angles of a polygon that share a side are consecutive angles.

Theorem 6.4

• If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Using Consecutive Angles

• What is the measure of angle P in parallelogram PQRS?A. 26°B. 64°C. 116°D. 126°

180m P m S

64 180m P

116m P

Theorem 6.5

• If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Theorem 6.6

• If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Using Algebra to Find Lengths

• Solve a system of linear equations to find the values of x and y in parallelogram KLMN. What are KM and LN?

Using Algebra to Find LengthsKP MP

LP NP10 2 8y x

2x y 10 2( 2) 8y y 10 2 4 8y y 10 4y

14 y14 2x

16x

2( )KM KP2( 10)KM y 2(14 10) 48

2( )LN LP2LN x2(16)32

Theorem 6.7

• If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Classifying Polygons by # of Sides# of Sides Name

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

8 Octagon

9 Nonagon

10 Decagon

11 Hendecagon

12 Dodecagon

Two Types of Polygons

Convex – all vertices point outward

Concave – at least one vertex points inward towards the center of the polygon (The side looks like it “caved” in)

Regular Polygons

A Regular Polygon is a polygon in which all sides are the same length.

Equilateral Triangle Square

Review of Similar Triangles

• 2 Triangles are similar if they have the same shape (i.e. the same angle in the same positions)

Similar Polygons

The same is true of polygons. 2 polygons are similar if they have the same angles in the same

positions (i.e. same shape)

^ Similar Pentagons ^

Similar Trapezoids

Similar Rectangles

60 120

120

6 6

50°

130°

Essential Question

• What are properties of sides and angles of rhombuses, rectangles, and squares?

Properties of Special Parallelograms• In this lesson, you will study three special

types of parallelograms: rhombuses, rectangles and squares.

A rhombus is a parallelogramwith four congruent sides

A rectangle is a parallelogram with four right

angles.

A square is a parallelogram with four congruent sides and four right angles.

Venn Diagram shows relationships-- MEMORIZE• Each shape has the properties of every group that it

belongs to. For instance, a square is a rectangle, a rhombus and a parallelogram; so it has all of the properties of those shapes.

RectanglesRhombuses

parallelograms

rhombuses rectangles

squares

Some examples of a rhombus

Examples of rectangles

Examples of squares

Ex. 1: Describing a special parallelogram• Decide whether the statement is always, sometimes, or never true.

a. A rhombus is a rectangle.

b. A parallelogram is a rectangle.

RectanglesRhombuses

parallelograms

rhombuses rectangles

squares

Ex. 1: Describing a special parallelogram Decide whether the statement is always, sometimes, or never true.

b. A parallelogram is a rectangle.

c. The statement is sometimes true. Some parallelograms are rectangles. In the Venn diagram, you can see that some of the shapes in the parallelogram box are in the area for rectangles, but many aren’t.

RectanglesRhombuses

parallelograms

rhombuses rectangles

squares

Family of Parallelograms

• Types of Parallelograms

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.

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!

Foldable

4. Write QUADRILATERALS down the left hand side

The fold crease

Foldable

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

The fold crease

6. Reopen the fold.

Foldable

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

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

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

Foldable

* Fold over the second cut section and write RECTANGLE on the outside.* Reopen the fold.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

Foldable

* On the left hand section, draw a rectangle.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

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

1. Special parallelogram.

2. Has 4 right angles

3. Diagonals are congruent.

Foldable

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

* Reopen the fold.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

1. Special parallelogram.

2. Has 4 right angles

3. Diagonals are congruent.

Foldable

* On the left hand section, draw a rhombus.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

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

1. Special parallelogram.

2. Has 4 right angles

3. Diagonals are congruent.

1. Special Parallelogram

2. Has 4 Congruent sides

3. Diagonals are perpendicular.

4. Diagonals bisect opposite angles

Foldable

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

* Reopen the fold.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

1. Special parallelogram.

2. Has 4 right angles

3. Diagonals are congruent.

1. Special Parallelogram

2. Has 4 Congruent sides

3. Diagonals are perpendicular.

4. Diagonals bisect opposite angles

Foldable

* On the left hand section, draw a square.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

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

* Place in your notebook and save for tomorrow.

1. Special parallelogram.

2. Has 4 right angles

3. Diagonals are congruent.

1. Special Parallelogram

2. Has 4 Congruent sides

3. Diagonals are perpendicular.

4. Diagonals bisect opposite angles

1. All the properties of parallelogram, rectangle, and rhombus

2. 4 congruent sides and 4 right angles

Foldable

* On the left hand section, draw a square.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

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

1. Special parallelogram.

2. Has 4 right angles

3. Diagonals are congruent.

1. Special Parallelogram

2. Has 4 Congruent sides

3. Diagonals are perpendicular.

4. Diagonals bisect opposite angles

1. All the properties of parallelogram, rectangle, and rhombus

2. 4 congruent sides and 4 right angles

Foldable

* On the left hand section, draw a kite.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Opposite sides are parallel

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

* Place in your notebook and save for tomorrow.

1. Special parallelogram.

2. Has 4 right angles

3. Diagonals are congruent.

1. Special Parallelogram

2. Has 4 Congruent sides

3. Diagonals are perpendicular.

4. Diagonals bisect opposite angles

1. All the properties of parallelogram, rectangle, and rhombus

2. 4 congruent sides and 4 right angles

1. The diagonals of a kite meet at a right angle.

(2) Kites have exactly one pair of opposite angles that are congruent.