Daily Do from last class Homework Answers 10 7 These are similar: What does y =? x =? 36 74 0 78 0 154 o 44 48 54 o y x 154 o 78 0 12 74 0 9 1. 8 ft 2. 21m 3. 21 ft 4. 30cm 5. 6mm 6. 16 in 7. yes 9 = 7 8. No 8 15 12 14 24 40 What is a tessellation???? Give an example... 1
LESSON 10 8 POLYGONS Objective: To be able to discover the formula to figure out the sum of the interior angles of any polygon. To use the interior angle sum to find missing angles of polygons. Virtue/Skill: Many of the geometric proofs that you will be proving in geometry will be using angles. Finding area and volume of solids that use polygons as bases requires knowledge of interior angles. 2
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Triangles will help you find the sum of the angles for ANY POLYGON. If we know the sum of the angles we can find the measure of just one angle of ANY REGULAR POLYGON. Please make a table: 5 columns across and 11 rows down polygons # of sides #of triangles sum of angles each angle measure 4
All triangles have a sum of 180 degrees in their angles If you divide a polygon into triangles you will discover how many degrees are in that polygon. A quadrilateral's angles add up to Draw lines, starting at a vertex going to every other vertex. Count the number of triangles Multiply the number of triangles by 180 to find the sum of the angles 5
360 A quadrilateral's angles add up to o Find the measure of one angle in a regular quadrilateral (square) sum of the angles number of angles 360 = 90 4 0 A pentagon's angles add up to Draw lines, starting at a vertex going to every other vertex. Count the number of triangles Multiply the number of triangles by 180 to find the sum of the angles Click Pentagon for Video 6
A pentagon's angles add up to 540 o Find the measure of one angle in a regular pentagon sum of the angles number of angles 540 = 108 5 0 A hexagon's angles add up to Draw lines, starting at a vertex going to every other vertex. Count the number of triangles Multiply the number of triangles by 180 to find the sum of the angles Click Hexagon for Video 7
A hexagon's angles add up to 720 o Find the measure of one angle in a regular hexagon sum of the angles number of angles 720 = 120 6 0 A heptagon's angles add up to Draw lines, starting at a vertex going to every other vertex. Count the number of triangles Multiply the number of triangles by 180 to find the sum of the angles Click Heptagon for Video 8
A heptagon's angles add up to 900 o Find the measure of one angle in a regular heptagon (round to the nearest tenth) sum of the angles number of angles 900 = 128.6 7 0 Have you noticed a pattern? 9
To find the number of degrees (sum of the angles) in any regular polygon: number of sides (n 2) 180 To find the measure of one angle in a regular polygon: sum of angles # of angles Name of polygon Number of sides Number of Triangles Sum of Angles One angle measure 3 1 x 180= 180 0 4 2 x 180= 360 0 5 3 x 180= 6 4 x 180= 7 5 x 180= 8 6 x 180= 9 7 x 180= 10 8 x 180= 10
Summary Objective: To be able to discover the formula to figure out the sum of the interior angles of any polygon. To use the interior angle sum to find missing angles of polygons. Virtue/Skill: Many of the geometric proofs that you will be proving in geometry will be using angles. Finding area and volume of solids that use polygons as bases requires knowledge of interior angles. Assignment: Workbook 10 8 Exit Question What is the missing angle measure? (figure not drawn to scale) 122 o 123 o? 115 o 109 o 80 o 11
Attachments pentagon.wmv hexagon.wmv heptagon.wmv