3-4 day 2 Review homework Worksheet Review worksheet Start notes for 3-5

m<BHD = 56 m<HDB = 58 m<HGI = 74 Find the measure of <DBH and <GCD. WARM UP on the little piece of paper

Homework Answers x = 30, y = x = 110, y = x = 40, y = x = 90, y = x = 40, y = x = 40, y = 30

Worksheet

3.5 Polygons Geometry Ms. Kelly Fall 2010

Objectives: Recognize and name convex polygons and regular polygons Find the measures of interior angles and exterior angles of convex polygons

Fun with notes! We will be taking notes like we did on Friday except you can keep it in your notebook. Fold page in half (hot dog). Fold in half again (you should have four squares). This will help your notes be more organized!

Definitions: Polygon – means “many angles” –Each segment intersects exactly two other segments, one at each endpoint. –No two segments with a common endpoint are collinear. Vertex – each endpoint of a side. Plural is vertices. You can name a polygon by listing its vertices consecutively. SIDE

Example 1: Identifying Polygons State whether the figure is a polygon. If it is not, explain why. Not D – has a side that isn’t a segment – it’s an arc. Not E– because two of the sides intersect only one other side. Not F because some of its sides intersect more than two sides. Figures A, B, and C are polygons.

Polygons are named by the number of sides they have …. Number of sides Type of Polygon 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon 8Octagon 9Nonagon 10Decagon 12Dodecagon nn-gon Try to draw and hexagon, then try to draw a dodecagon. What do you start to notice about the angles?

Convex or concave? Convex if no line that contains a side of the polygon contains a point in the interior of the polygon. Concave or non-convex if a line does contain a side of the polygon containing a point on the interior of the polygon. See how it doesn’t go on the Inside-- convex See how this crosses a point on the inside? Concave.

Warm up (write the answers on a little piece of paper) Open up your books to page 103 and do Convex polygon 2.Nonconvex polygon 3.Not a polygon 4.Nonconvex polygon 5.Not a polygon 6.Nonconvex polygon Fun question: What famous person would you like to meet?

Identifying Regular Polygons Regular polygons are equilateral and equiangular (all sides AND angles are congruent) Decide whether the following polygons are regular. Equilateral, but not equiangular, so it is NOT a regular polygon. Heptagon is equilateral, but not equiangular, so it is NOT a regular polygon. Pentagon is equilateral and equiangular, so it is a regular polygon.

Interior angles of quadrilaterals A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Polygon PQRST has 2 diagonals from point Q, QT and QS diagonals How many triangles do you see? What does a triangle add up to? The following gives us an important theorem…

Theorems! Theorem 3-13 The sum of the measures of the angles of a regular convex polygon with n sides is (n – 2)180. Theorem 3-14 The sum of the measures of the exterior angles of any convex polygon, one angle at each angle at each vertex, is 360.

Example A regular polygon has 12 sides. Find the measure of: -the interior angle sum -each interior angle -each exterior angle Solution: The interior angle sum (12-2)*180 = 1800 Each interior angle is 1800/12 = 150 Each exterior angle is 360/12 = 30

Complete the table (you may put this anywhere in your notes) Fill in the table on page #9 Number of sides61020 Measure of each ext. angle 1020 Measure of each int. angle 17990

To find the number of sides if given an exterior angle: 10 = 360/n (Solve for n) When you get n, you can find the interior angle To find the number of sides if given an interior angle: 180 – interior angle, then repeat first example

Closure Find the measure an interior angle for the following: –Regular quadrilateral –Regular octagon –Regular polygon with 15 sides –Regular polygon with 20 sides

Classwork Complete the worksheet and hand in for a grade. Homework: page , 8-11