PIB Geometry 3-5: Polygons.

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Presentation transcript:

PIB Geometry 3-5: Polygons

Homework 3-4 Questions?

3-5 Objectives Recognize and name convex polygons and regular polygons. Investigate and apply the Polygon Interior Angle Sum Theorem. Investigate and apply the Polygon Exterior Angle Sum Theorem.

Angles of a Polygon Investigation Partner up!

Theorem 3-13: Polygon Interior Angle Sum Theorem The sum of the measures of the interior angles of a convex polygon with 𝑛 sides is: Theorem 3-14: Polygon Exterior Angle Sum Theorem The sum of the measures of the exterior angles of a convex polygon with 𝑛 sides is:

In case you missed it:

Examples Find the sum of the measures of the interior angles of a heptagon. Find the sum of the measures of the exterior angles of a heptagon.

Def: A polygon is regular if it is both equilateral and equiangular. What is the measure of each interior angle of regular n-gon? Each exterior angle?

Examples. Solve for 𝑚∠𝐴

Example The measure of one interior angle of a regular polygon is 5 12 the sum of the measures of its exterior angles. How many sides does the polygon have?

Example The sum of the measures of the interior angles of a regular polygon is 24 times the measure of one exterior angle. How many sides does the polygon have?

Polygons