Date: 8.1(a) Notes: Polygon Interior Angles Sum Lesson Objective: Find and use the sum of the measures of the interior angles of a polygon. CCSS: G.MG.1.

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Presentation transcript:

Date: 8.1(a) Notes: Polygon Interior Angles Sum Lesson Objective: Find and use the sum of the measures of the interior angles of a polygon. CCSS: G.MG.1

Lesson 1: Anatomy of a Polygon Polygon: A closed plane figure formed by 3 or more straight segments that intersect only at their endpoints.

Lesson 1: Anatomy of a Polygon Types of Polygons: Know these on p. 476!

Lesson 1: Anatomy of a Polygon Regular: All sides and all angles are congruent. Irregular: A polygon that is not regular. Concave: When a diagonal contains points outside of the polygon. Convex: When no diagonals contain points outside of the polygon.

Lesson 1: Anatomy of a Polygon Plot a point P. Construct regular hexagon ABCDEF inscribed in a circle with diameter 3”.

Lesson 1: Anatomy of a Polygon Label as follows. Interior Vertex Angle Side Diagonal Exterior Angle

Lesson 1: Anatomy of a Polygon Measure an interior angle. _____ What would the sum of the interior angles be? ____ Interior Vertex Angle Side Diagonal Exterior Angle

Lesson 2: Polygon Interior Angles Sum Use a ruler to draw the following: Triangle Quadrilateral Pentagon

Lesson 2: Polygon Interior Angles Sum Starting at one vertex, draw diagonals to each of the remaining vertices. Triangle Quadrilateral Pentagon

Lesson 2: Polygon Interior Angles Sum What is the sum of the interior angles in each figure? Can you come up a formula? Triangle Quadrilateral Pentagon

Lesson 2: Polygon Interior Angles Sum Triangle Quadrilateral Pentagon The sum of the interior angle measures of an n-sided convex polygon is (n – 2)180.

Lesson 2: Polygon Interior Angles Sum Example: The number of sides = ____ The sum of the interior angles is: ( __ – 2)180 =

Lesson 3: Finding the Interior Angle Measures and Sums in Polygons A.Find the sum of the interior angle measures of a regular convex heptagon. B.Find the measure of each interior angle of a regular convex heptagon.

Lesson 4: Using Algebra to Find the Interior Angle Measures and Sums in Polygons Find the measure of each interior angle of pentagon ABCDE.

8.1(a): Do I Get It? 1.Name the polygon by the number of sides. Then tell whether it is regular or irregular, concave or convex. 2.Find the sum of the interior angle measure of a convex 11-gon. 3.Find the measure of each interior angle measure of a regular 11-gon.