1. Warm UP: 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.

2. Polygons are named by the number of sides they have – MEMORIZE
Type of Polygon 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon

3. Polygons are named by the number of sides they have – MEMORIZE
Type of Polygon 8
Octagon 9
Nonagon 10
Decagon 12
Dodecagon n
n-gon

4. Convex or concave? CONCAVE CONVEX
Identify the polygon and state whether it is convex or concave.
CONCAVE
CONVEX

5. Identifying Regular Polygons
Heptagon is equilateral, but not equiangular, so it is NOT a regular polygon.
Decide whether the following polygons are regular.
Pentagon is equilateral and equiangular, so it is a regular polygon.
Equilateral, but not equiangular, so it is NOT a regular polygon.

6. 6.1 Polygons Objectives: Identify, name, and describe polygons
Use the sum of the measures of the interior angles of a quadrilateral.

7. Theorem 6.1: Interior Angles of a Quadrilateral
The sum of the measures of the interior angles of a quadrilateral is 360°.
m1 + m2 + m3 + m4 = 360°

8. Ex. 1: Use the information in the diagram to solve for x.
80°
70°
2x° x°
x°+ 2x° + 70° + 80° = 360°
3x = 360
3x = 210
x = 70
Sum of the measures of int. s of a quadrilateral is 360°
Combine like terms
Subtract 150 from each side.
Divide each side by 3.

9. Ex. 2: Use the information in the diagram to solve for x.
5x + 7x = 360
12x = 360
12x = 240
X = 20 50 7x 5x 70

10. Ex. 3: Use the information in the diagram to solve for x.87 93

11. Ex. 4: Use the information in the diagram to solve for x.
3x + 2x + 3x + 2x = 360
10x = 360
x = 36 2x 3x 3x 2x

12. Ex. 5: Find the measure of each angle in the parallelogram.
2x + 4x +2x + 4x = 360
12x = 360
x = 30
Substitute
2(30) = 60
4 (30) = 120 2x 4x 2x 4x

13. Assignment Solve the remaining problems independently
Reminder: 2nd Nine weeks benchmark on Thursday