7-5 Polygons

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

7-5 Polygons

Warm Up

1. How do you name a ray? Under the raysymbol, name first the endpoint and thenany other point on the ray.

2. What is the measure of an obtuse angle?between 90° and 180°

3. How do you name a line?Under the line symbol, name any twopoints on a line.

4. What is true of supplementary angles?The sum of their measures is 180°.

Problem of the Day

Draw a polygon with 10 congruent sides. Make 5 of the angles acute angles and the other 5 reflex angles (greater than 180°).

Possible answer:

Course 2

7-5 Polygons

Learn to identify and name polygons.

Course 2

7-5 Polygons

Vocabulary

polygonsidevertex of a polygonregular polygon

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Course 2

7-5 Polygons

Course 2

7-5 Polygons

Triangles and rectangles are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. Each line segment forms a side of the polygon, and meets, but does not cross, another line segment at a common point. This common point is a vertex of a polygon.

The polygon atleft has sixsides and sixvertices.

Vertices is plural for vertex.

Remember!

Side

Vertex

Determine whether each figure is a polygon. If it is not, explain why not.

Additional Example 1A & 1B: Identifying Polygons

Course 2

7-5 Polygons

A. B.

The figure is a polygon. It is a closed figure with 4 line segments.

The figure is not a polygon. It is not a closed figure.

Determine whether each figure is a polygon. If it is not, explain why not.

Additional Example 1C & 1D: Identifying Polygons

Course 2

7-5 Polygons

C. D.

The figure is not a polygon. The figure is not formed by line segments.

The figure is not a polygon. There are line segments in the figure that cross.

Determine whether each figure is a polygon. If it is not, explain why not.

Try This: Example 1A & 1B

Course 2

7-5 Polygons

A. B.

The figure is a polygon. It is a closed figure with 5 line segments.

The figure is not a polygon. It is not a closed figure.

Determine whether each figure is a polygon. If it is not, explain why not.

Try This: Example 1C & 1D

Course 2

7-5 Polygons

C. D.

The figure is not a polygon. The figure is not formed by line segments.

The figure is not a polygon. There are line segments in the figure that cross.

Course 2

Polygons7-5

Polygons are classified by the number of sidesand angles they have.

Triangle3 sides

3 angles

Quadrilateral4 sides

4 angles

Pentagon5 sides

5 angles

Hexagon6 sides

6 angles

Heptagon7 sides

7 angles

Octagon8 sides

8 angles

Nonagon9 sides

9 angles

Decagon10 sides

10 angles

Name each polygon.

Additional Example 2: Classifying Polygons

Course 2

7-5 Polygons

A.

Octagon

B.

Quadrilateral

Try This: Example 2

Name each polygon.

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7-5 Polygons

A. B.

Quadrilateral Pentagon

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Course 2

7-5 Polygons

A regular polygon is a polygon in which all sides are congruent and all angles are congruent.

Additional Example 3: Identifying and Classifying Regular Polygons

Course 2

7-5 Polygons

Name each polygon and tell whether it is aregular polygon. If it is not, explain why not.

The figure is a regularquadrilateral. A regular quadrilateral is also called a square.

The figure is aquadrilateral. It is not a regular polygon becauseall of the sides are not congruent.

A. B.

Try This: Example 3

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Course 2

7-5 Polygons

The figure is a triangle. It is not a regular polygon because all sides and angles are not congruent.

The figure is a regular triangle.

Name each polygon and tell whether it is aregular polygon. If it is not, explain why not.

A. B.

Lesson Quiz

Determine whether each statement is true or false.

1. Every polygon is a closed figure.

2. Every open figure is a polygon.

3. A pentagon with sides lengths of 10 units and angles measuring 108° is a regular polygon.

4. A quadrilateral with side lengths of 10, 12, 10, and 12 units is a regular polygon.

5. What is the name of a five-sided polygon?

false

true

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true

false

Course 2

7-5 Polygons

pentagon