Polygons and Symmetry Lesson 1

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Presentation transcript:

Polygons and Symmetry Lesson 1 You need a piece of paper off of the side counter and markers or colored pencils today.

Do Now A 24 foot ladder leaning against a wall reaches 19.5 feet up the wall. At what angle does the bottom of the ladder meet the ground? 2. How many total degrees are in a square?

Polygons Notes convex concave A polygon is a closed two-dimensional figure with straight sides. Polygon Not A Polygon convex concave

Polygons Notes A regular polygon is a convex polygon with all sides and all angles congruent. Regular Irregular

Polygons Notes Important Polygons Formulas!! Sum of Interior Angles Exterior Angles One Interior Angle One Exterior Angle Only for regular polygons Only for regular polygons

Class Example 1 What is the measure of one interior angle of a regular octagon? What is the measure of one exterior angle of a regular octagon?

Find the missing angle measure of the irregular polygon below. Class Example 2 Find the missing angle measure of the irregular polygon below.

Class Example 3 Solve for x.

Class Example 4 Find: ∠2 = ______ ∠4 =_______ ∠5 = ______ ∠6 = ______ Given: ∠1 = 70° ∠4≅∠5 ∠3 = 80° AB is parallel to FG Find: ∠2 = ______ ∠4 =_______ ∠5 = ______ ∠6 = ______ ∠7 = ______

Figure ABCDEF is a regular hexagon. What is the measure of ∠FEG. Student Example 1 Figure ABCDEF is a regular hexagon. What is the measure of ∠FEG.

Student Example 2 The sum of the measures of the interior angles of a polygon is 1260°. How many sides does the polygon have?

What is the measure of angle 1? Student Example 3 What is the measure of angle 1?

Polygons Practice What is the sum of the interior angles of an octagon? What is the sum of the interior angles of a dodecagon (12 sides)? What is the measure of one interior angle of a regular decagon? What is the measure of one interior angle of a regular 11-gon? 5. How many sides does a polygon have if the sum of its interior angles is 1080? 6. How many sides does a polygon have if the sum of its interior angles is 3420? 7. Solve for x.