2.  Some sequences of geometric objects change in predictable ways.  Some angles have special relationships based on their position or measure.  Polygons can be described uniquely by their sides and angles.

3.  Draw a triangle on a piece of paper.  Find the measure of each of the 3 angles in your triangle.  Compare your angle measures with those of your table group. What patterns or relationships do you observe?

4.  Other than by measuring, how could we prove that the measures of the angles in a triangle add up to 180 o ?

5.  Draw a triangle on a notecard.  Cut out the triangle.  Label each vertex of the triangle (close to the vertex)  Cut off the vertices of the triangle.  Put them together.  What do you get?

7.  Use the Parallel Postulate (p. 604) › Look at figure 10.22 on p. 605  What do we know?  What does this tell us? 425 13 l m A BC Line l is parallel to line m

8.  Draw a triangle on a piece of paper.  What is the sum of the angle measures of the 3 exterior angles in your triangle?  Compare your results with those of your table group, and make a conjecture.  How could you prove your conjecture? 1 2

9.  On a post-it, write a conjecture for what you think the rule might be for finding the measure of the exterior angles of any polygon.  How might you prove your conjecture?

10.  Method 1: Cut out exterior angles  Method 2: Walk-and-Turn  Method 3: Use the relation with the sum of the interior angles

11.  Quadrilaterals › In your groups, draw a quadrilateral. › Measure each angle. › Find the sum of the angle measures. › Record your result.  Repeat with a polygon with more than 4 sides.

12. SidesTotal Angle MeasureAvg. Angle Measure 3180°60° 4 5 6 7 8

13.  What pattern(s) do you notice?  What conjecture can you make?  How could you prove your conjecture?

14.  There are 3 approaches for determining the measure of the interior angles of a polygon: › Find the triangles with a common vertex at one vertex of the polygon › Find the triangles with a common vertex in the center of the polygon › Walk and Turn

15.  Section 10.3: #’s 15, 16, 22, 41, 42, 43, 47, 49  Turn in #’s 15, 16, 42, & 47