1. Properties and Attributes of Polygons
Geometry 6.1
Properties and Attributes of Polygons

2. Learning Targets Students should be able to…3
Classify polygons based on their sides and angles.
Find and use the measures of interior and exterior angles of polygons.

3. Warm-up
1. What is the sum of the measures of the interior angles of a triangle? 2. Two angles in a triangle measure 34° and 53°. The third angle measures x°. What is x? 3. In which kind of triangle are all three sides congruent? 4. In which kind of triangle are all three angles

4. Go over Test/Grades
Pass out homework packets.
Look over tests.

5. What do you already know?
Name the polygon with the number of sides…
3 9
6 n 7 8
See what you can remember. We will go over later in the notes.

6. Vocabulary Term Name Diagram Additional Notes Side of a polygon
𝐴𝐵 is a side of the polygon.
Segments that form a polygon C B D A E

7. Vocabulary Term Name Diagram Additional Notes Side of a polygon
𝐴𝐵 is a side of the polygon.
Segments that form a polygon
Vertex of polygon
A is a vertex
See above diagram
The common endpoint of two sides C B D A E

8. Vocabulary Term Name Diagram Additional Notes Side of a polygon
𝐴𝐵 is a side of the polygon.
Segments that form a polygon
Vertex of polygon
A is a vertex
See above diagram
The common endpoint of two sides
Diagonal
𝐴𝐶 is a diagonal.
A segment that connects any two nonconsecutive vertices. C B D A E C B D A E

9. Vocabulary Term Name Diagram Additional Notes Side of a polygon
𝐴𝐵 is a side of the polygon.
Segments that form a polygon
Vertex of polygon
A is a vertex
See above diagram
The common endpoint of two sides
Diagonal
𝐴𝐶 is a diagonal.
A segment that connects any two nonconsecutive vertices.
Regular polygon
A polygon that is both equilateral and equiangular. C B D A E C B D A E

10. Vocabulary Term Name Diagram Additional Notes Concave
Concave equilateral
When any points of the quadrilateral lie in the exterior of the polygon.

11. Vocabulary Term Name Diagram Additional Notes Concave
Concave quadrilateral
When any points of the quadrilateral lie in the exterior of the polygon.
Convex
Convex quadrilateral
No diagonal contains points in the exterior of the polygon.

12. Review of Vocabulary 2. 1. 3.

13. Define: Polygon
A polygon is a plane figure that meets the following conditions:
It is formed by three or more segments called sides.
Each side intersects exactly two other sides, at each endpoint

14. Vertex
Each endpoint of a side is a vertex of the polygon. The plural of vertex is vertices.
You can name a polygon by listing its vertices consecutively.

15. Practice!

16. Revisiting Names of Polygons
What did you remember?
# of sides Type of Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n n-gon

17. Regular and Irregular Polygon
a polygon that is both equilateral and equiangular
Irregular Polygon:
a polygon that is not regular

18. Examples

19. Concave verse Convex Convex:
No diagonal contains points outside of the polygon.
*All diagonals inside the polygon
Concave:
if any part of a diagonal contains points in the exterior of the polygon.
*At least one diagonal outside the polygon

20. Examples

21. Polygon Angle Sum Theorem
The sum of the interior angle measures of a convex polygon with n sides is
(n – 2)180°

22. Polygon Angle Sum Theorem Practice
a. Find the sum of the interior angle measures of a convex octagon.

23. Polygon Angle Sum Theorem Practice
b. Find the measure of each interior angle of a regular nonagon.

24. Polygon Angle Sum Theorem Practice
c. Find the measure of each interior angle of quadrilateral PQRS.

25. Practice

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