1. Objective: Explore Interior Angles of Polygons

2. Interior Angles
An interior angle is an angle formed by two sides of a polygon with a common vertex.
A triangle has three interior angles

3. Triangle Explore Activity
Draw a large-ish triangle on one of your half sheets using a ruler.
Cut your triangle out.
Tear off the three corners of the triangle.
Rearrange the angles so their sides are adjacent and their vertices meet at a point

4. What do you notice?
The sum of the interior angles of a triangle add to __________

5. Explore Angles in a Quadrilateral
Draw a large-ish quadrilateral on one of your half sheets using a ruler.
Cut your quadrilateral out.
Tear off the four corners of the quadrilateral.
Rearrange the angles so their sides are adjacent and their vertices meet at a point

6. What do you notice?
The sum of the interior angles of a quadrilateral add to __________

7. I need a Volunteer!
Draw as many parallel lines to line l as you can that go through point P P l

8. Parallel Postulate
Through a point P not on line l, there is exactly one line parallel to l.

9. An auxiliary line is a line that is added to a figure to aid in a proof.
An auxiliary line used in the Triangle Sum Theorem. Line l is parallel to line segment AC. We can draw this auxillary line because of the parallel postulate (there is only one line parallel to line segment AC that goes through point B)

10. What is the sum of the measures of angles 4, 2, and 5?
How are angles 1 and 4 related?
How are angles 5 and 3 related?
How might we write a proof using all of this information?

11. pg. 1083

12. Polygon- a closed figure having three or more sides and lying on one plane

13. 11 sides= hendecagon

14. Fun Facts!
11 hendecagon 12 dodecagon 13 triskaidecagon or tridecagon 14 tetrakaidecagon or tetradecagon 15 pendedecagon 16 hexdecagon 17 heptdecagon 18 octdecagon 19 enneadecagon 20 icosagon but you can just say 13-gon

15. Each segment that forms a polygon is a side of the polygon
Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.

16. A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex.
OR we can say a polygon is concave if it has one or more interior angles greater than 180°, convex if it does not

17. All the sides are congruent in an equilateral polygon
All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular.

18. From now on we will only be talking about convex polygons!

19. Draw the diagonals from any one vertex of the polygon
Draw the diagonals from any one vertex of the polygon. How many triangles are formed?
pg. 1084

20. Fill in the Chart!
pg. 1084

21. Complete C, D on pg. 1085

22. Find x
“It’s Right Here!”
X = 158

23. Each exterior angle has two remote interior angles
Each exterior angle has two remote interior angles. A remote interior angle is an interior angle that is not adjacent to the exterior angle.
4 is an exterior angle.
The remote interior angles of 4 are 1 and 2.
Exterior
Interior
3 is an interior angle.

24. What is the relationship between angle 4 and angles 1 and 2?
Exterior
Interior
pg. 1087

25. Write a Paragraph Proof!

26. 50°
115°
65° 3 4

27. Find mB
x = 26
mB = 2x + 3 = 2(26) + 3 = 55°

28. Your turn! pg and 12

31. Find the measure of all exterior angles.
What is their sum?

32. Find the measure of all exterior angles.
What is their sum?

34. Find the measure of each exterior angle of a regular 20-gon.
A 20-gon has 20 sides and 20 vertices.
sum of ext. s = 360°.
measure of one ext.  =
The measure of each exterior angle of a regular 20-gon is 18°.

35. Find the value of b in polygon FGHJKL.
15b° + 18b° + 33b° + 16b° + 10b° + 28b° = 360°
120b = 360
b = 3

36. Angle Chasing

37. Homework
Angle Chasing WS
pg (1-9)
Pg (10-15)