1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
1. How do you name a ray?
Under the ray
symbol, name first the endpoint and then
any 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 two
points on a line.
4. What is true of supplementary angles?
The sum of their measures is 180°.

3. Preparation for MG2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).
California
Standards

4. Vocabulary
polygon
vertex
regular polygon

5. Triangles and rectangles are examples of 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. Each side meets exactly two other sides, one on each end, in a common endpoint. Each endpoint is a vertex of the polygon.
Side
Vertex
The polygon at
left has six
sides and six
vertices.
Vertices is plural for vertex.
Remember!

6. Additional Example 1: Identifying Polygons
Determine whether each figure is a polygon. Explain your answer. 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.

7. Additional Example 1: Identifying Polygons
Determine whether each figure is a polygon. Explain your answer. C. D.
The figure is not a polygon. The figure is not formed by line segments.
The figure is not a polygon. There are sides that meet more than 2 other sides.

8. Check It Out! Example 1
Determine whether each figure is a polygon. Explain your answer. 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.

9. Check It Out! Example 1
Determine whether each figure is a polygon. Explain your answer. C. D.
The figure is not a polygon. The figure is not formed by line segments.
The figure is not a polygon. There are sides that meet more than two other sides.

10. Polygons are classified by the number of sides and angles they have.
Triangle
3 sides
3 angles
Quadrilateral
4 sides
4 angles
Pentagon
5 sides
5 angles
Hexagon
6 sides
6 angles
Heptagon
7 sides
7 angles
Octagon
8 sides
8 angles
Nonagon
9 sides
9 angles
Decagon
10 sides
10 angles

11. Additional Example 2: Classifying Polygons
Name each polygon. A. B.
8 sides, 8 angles
4 sides, 4 angles
Octagon
Quadrilateral

12. Check It Out! Example 2
Name each polygon. B. A.
4 sides, 4 angles
5 sides, 5 angles
Quadrilateral
Pentagon

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

14. Additional Example 3: Identifying and Classifying Regular Polygons
Name each polygon and tell whether it is a
regular polygon. Explain your answer. B. A.
The figure is a
quadrilateral. It is not a
regular polygon because
all of the sides are not
congruent.
The figure has congruent angles and congruent sides. It is a regular quadrilateral.

15. A polygon with congruent sides is not necessarily a regular polygon
A polygon with congruent sides is not necessarily a regular polygon. Its angles must also be congruent.
Caution!

16. Check It Out! Example 3
Name each polygon and tell whether it is a
regular polygon. If it is not, explain why not. B. A.
The figure has congruent angles and congruent sides. It is a regular triangle.
The figure is a triangle. It is not a regular polygon because all sides and angles are not congruent.

17. Lesson Quiz: Part I
Determine whether each figure is a polygon. If it in not, explain why not. Name each polygon.
yes; pentagon
no; open figure
yes; octagon
no; curved lines

18. Lesson Quiz: Part II
5. Tell whether each figure on the previous slide is a regular polygon. If it is not, explain why not.
1: No, all sides and angles are not congruent.
2, 4: No, they are not polygons.
3: yes