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# Math 112b chapter 9 section 2 day 1 (2/22/2016) Math 112b Sec 004

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This 3 page Class Notes was uploaded by amber weiss on Tuesday February 23, 2016. The Class Notes belongs to Math 112b Sec 004 at Southern Illinois University Edwardsville taught by cheryl eames in Spring 2016. Since its upload, it has received 21 views. For similar materials see elementary mathmatics in Mathmatics at Southern Illinois University Edwardsville.

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Date Created: 02/23/16

Math 112b Chapter 9 Section 2 02/22/2016 Upcoming: a) Quiz #3 on Wednesday February 24, 2016 b) Comp Quiz #2 on Monday February 29, 2016 c) Test #2 on Wednesday March 2, 2016 1. Describe how you would help students discover the sum of measures of the 3 angles in a triangle. - Measure the angles and add them up (need to know how to use a tool) - Cut, tear the corners of the triangle, stack and see which one is larger ; make another shape, in this case a line. - Rule: a straight line = 180 degrees 2. What must students know before completing number 1? - How to use the tool (protractor) - That a straight line is 180 degrees 3. How can we expand problem 1 to find the sum of measures of the 4 angles in a quadrilateral? - First, we draw a quadrilateral (4 sided figure) - Then, we cut a diagonal from one of the vertexes. - We should be able to see 2 triangles - The black dots represent vertex - the black line represents the diagonal to see the 2 triangles 6 5 2 4 1 3 - M<1+m<2+m<3 = 180 - M<4+ m<5+ m<6 = 180 - M<all = 180+180 = 360 degrees - CONNECT NONADJACENT VERTICES WITH A DIAGANOL - Sum of angles = vertex angle 4. Name # of sides # of triangles Sum of angles Triangle 3 180 1 Quadrilateral 4 360 2 Pentagon 5 540 3 Hexagon 6 720 4 Heptagon 7 900 5 Octagon 8 1080 6 Nonagon 9 7 1260 Decagon 10 8 1440 Dodecagon 12 10 1800 n-gon n (n-2) (n-2) * 180 5. WE SKIPPED NUMBER 5 2 plane figures are congruent if… They are same size and shape Place 1 on other so they coincide Segments are congruent if… Same length Angles are congruent if… Same measure Figures are congruent if… Corresponding sides are congruent Corresponding angles are congruent 6. In each of the following diagrams, explain why they are not regular polygons. a) not congruent sides or angles b) sides are not congruent c) not even a polygon, doesn’t have sides or angles Central angle 7. verte Exterior angle x Name Sum of Vertex angle Central Angle Exterior angle angles Equilateral 180 180/3 = 60 360/3 = 120 180-60=120 Triangle Square 360 360/4 = 90 360/4= 90 180-90=90 Regular Pentagon 540 540/5 = 108 360/5= 72 180-108=72 Regular Hexagon 720 720/6= 120 360/6= 60 180-120=60 Regular Heptagon 900 900/7= 128.6 360/7= 51 180-128.6=51.4 Regular Octagon 1080 1080/8= 135 360/8= 45 180-135=45 Regular Nonagon 1260 1260/9= 140 360/9= 40 180-140=40 Regular Decagon 1440 1440/ 10= 360/10= 36 180-144=36 144 Regular 1620 1620/12= 135 360/12= 30 180-135=45 Dodecagon Regular n-gon (n-2) * 180 Total degrees/ A circle= 360/ 180- vertex number of angle straight number of sides sides line=180 8. The graph above is #8 9. HOMEWORK 10.HOMEWORK

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