Preview Warm Up California Standards Lesson Presentation

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°.

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

Vocabulary polygon vertex regular polygon

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!

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.

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.

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.

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.

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

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

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

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 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.

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!

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.

Lesson Quiz: Part I Determine whether each figure is a polygon. If it in not, explain why not. Name each polygon. 1. 2. 3. 4. yes; pentagon no; open figure yes; octagon no; curved lines

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