Do Now Take out your calculator. Take a protractor from the front.

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POLYGONS 10/17/2007 NAMING POLYGONS

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Presentation transcript:

Do Now Take out your calculator. Take a protractor from the front. In your notebook answer the following questions: How many sides does a pentagon have? Draw a hexagon. What shape has 7 sides?

Compton Jr. Posse

Polygon Sum Conjecture

Today’s Objectives Discover the sum of the angle measures in a polygon Write formulas for the measure of the interior angle of an equiangular polygon. Use problem solving skills

Polygons Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon 11—gon Dodecagon 13—gon N-gon

Investigation Draw the polygon. Carefully measure all the interior angles, then find the sum. Share your results with your group. If you measured carefully, you should all have the same sum! If your answers aren’t exactly the same, find the average. Copy the table. Repeat steps 1 and 2 for different polygons. # of sides of polygon 3 4 5 6 7 8 … n Sum of measures of angles

Quadrilateral sum Conjecture The sum of the measures of the four interior angles of any quadrilateral is _____. 360o .

Pentagon sum Conjecture The sum of the measures of the five interior angles of any pentagon is _____. 540o .

Polygon Sum Conjecture How many sides? How many triangles? How many degrees?

Polygon sum Conjecture The sum of the measures of the n interior angles of any n—gon is _____. 180o(n—2) .

Regular Polygons Regular Polygons—Equilateral and equiangular Equilateral—all n sides are congruent. Equiangular—all n interior angles are congruent.

Regular polygons. Find the measure of each interior angle.

Polygon sum Conjecture In a regular polygon, the measure of each interior angle of any n—gon is _____. 180o(n—2) . n

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Today’s Objectives Discover the sum of the angle measures in a polygon Write formulas for the measure of the interior angle of an equiangular polygon. Use problem solving skills

Exit Slip In each problem, show your work AND explain your reasoning. How many degrees are in a 45-gon? Include in your explanation what each part of the formula represents. What is the measure of each angle of a regular octagon? Find the measure of x.

Honors Exit Slip In each problem, show your work AND explain your reasoning. How many degrees are in a 45-gon? Include in your explanation what each part of the formula represents. What is the measure of each angle of a regular octagon? Find the measure of w, x, y, and z.