1. Figure 1: Triangle Review
Triangle Types
Name
Property
Angle
Angle
Sum of Interior Angles =_______ degrees for a triangle
Interior + Exterior angle =_______ degrees for a triangle

2. Figure 2: Interior / Exterior Angles
Draw and label an exterior angle and interior angle for each figure

3. Figure 3: Interior Triangles
Draw and label all interior angles for each figure
(both the quadrilaterals and the triangles)
Each quadrilateral has __________ triangles inside
For each quadrilateral, the sum of the interior angles equals _______ degrees
What is the relationship between the number of triangles and the sum of the interior angles? __________________________________________________

4. Figure 4: Interior Triangles
Draw interior triangles for each polygon starting from the same vertex each time.
Draw all interior angles for both the polygon and the triangles

5. Total number of degrees
Figure 5: Activity
Fill in the blanks in column 1 (number of sides)
Fill in rows 2 through 7 for column 2 (Number of triangles), and column three (Total number of degrees)
Try to determine a general formula (last two rows) ID
Number of sides
Number of triangles
Total number of degrees 1
3 (Triangle)
180 2
4 (Quadrilateral) 3
5 (_____agon) 4
6 (_____agon) 5
7 (_____agon) 6
8 (_____agon) 7
10 (____agon) 8
100 9 N

6. Figure 5a: Guided Practice
Find the sum of the interior angles for each figure (feel free to use the triangle method). 3 2 1 4
Confirm your answer to 2 and 3 by using a protractor (record each angle measured)
Please write the formula for determining the sum of the interior angles of a polygon:
Sum = ____________
Please re-write the formula as a sentence
__________________________________________________
If the sum of the interior angles of a polygon is 1620 deg, how many sides does it have?
_________
For an infinite sided polygon, what is the sum of the interior angles?__________
What is another name for an infinite sided polygon?___________

7. Figure 6: Summation Baseline questions (all must answer)
1. What are the sums of the interior angles for any polygon (formula)?
2. Does the answer change if the polygon is regular or irregular?
Homework Problem
3. Does the answer change if the polygon has a concave angle?
(Show example to support your answer)

8. Figure 7: Quiz
1. Draw and label an exterior angle and interior angle for each polygon below
2. Determine the number of triangles that will fit into each polygon above
3. Determine the sum of the interior angles for each polygon above
4. Write a general formula for the sum of the interior angles for a polygon
5. Does the formula change for regular vs irregular convex polygons?