Classify each quadrilateral below with its best name.

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Presentation transcript:

2 1 4 3 6 5 Classify each quadrilateral below with its best name. rhombus 1 Isosceles Obtuse Triangle 4 3 rectangle Scalene Right Triangle trapezoid 6 5 Acute Equilateral Triangle

Ch. 7-5 Angles and Polygons

Ch. 7-5 Angles and Polygons Here is a list of Common Polygons: Polygon Name Number of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Dodecagon 12

-Two consecutive sides of a polygon form one interior angle -Two consecutive sides of a polygon form one interior angle. The sum of the measures of the interior angles depends on the number of sides. -For a polygon with n sides, the sum of the measures of the interior angles is (n – 2)1800 Example 1: Find the sum of the measures of the interior angles of each figure below. Remember to use the formula. a.) nonagon b.) heptagon A nonagon has 9 sides so plug in 9 for n (9 – 2)180 = 7(180) = 1,2600 A heptagon has 7 sides so plug in 7 for n (7 – 2)180 = 5(180) = 9000

Example 2: Find the missing angle measure in the figures below. a. First find the sum of the measures of the interior angles. (5 – 2)180 = 5400 1300 920 750 Now add up all of the angle measures that you know and subtract it from 5400 to find out the measure of the missing angle. 130 + 75 + 102 + 92 = 399 540 – 399 = 1410 1020 x0 b.) A hexagon has 5 angles with measures of 1420, 840, 1230, 900, and 1300. What is the measure of the 6th angle? First find the sum of the measures of the interior angles. (6 – 2)180 = 7200 Now add up all of the angle measures that you know and subtract it from 7200 to find out the measure of the missing angle. 142 + 84 + 123 + 90 + 130 = 569 720 - 569 = 1510

-A regular polygon is a polygon with all sides congruent and all angles congruent. -To find the measure of each angle of a regular polygon, divide the sum of the angle measures by the number of angles. Example 3: Find the measure of each angle for the regular polygons below. a.) a regular octagon b.) a regular decagon First find the sum of the measure of the interior angles: (8 – 2)180 = 10800 First find the sum of the measure of the interior angles: (10 – 2)180 = 14400 Now divide 1080 by 8. Therefore every angle in a regular octagon is 1350 Now divide 1440 by 10. Therefore every angle in a regular dodecagon is 1440

HW – Pg. 326 Problem #’s 1-5 all, 8-20, 24-28 even