Geometry 6.1

Properties and Attributes of Polygons

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.

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 congruent?

Go over Test/Grades

• Pass out homework packets.

• Look over tests.

What do you already know?

• Name the polygon with the number of sides…3 9 4 105 126 n78

See what you can remember. We will go over later in the notes.

VocabularyTerm Name Diagram Additional Notes

Side of a polygon is a side of the polygon.

Segments that form a polygon

A

B

C

D

E

VocabularyTerm Name Diagram Additional Notes

Side of a polygon 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

A

B

C

D

E

VocabularyTerm Name Diagram Additional Notes

Side of a polygon 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 is a diagonal. A segment that connects any two nonconsecutive vertices.

A

B

C

D

E

A

B

C

D

E

VocabularyTerm Name Diagram Additional Notes

Side of a polygon 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 is a diagonal. A segment that connects any two nonconsecutive vertices.

Regular polygon A polygon that is both equilateral and equiangular.

A

B

C

D

E

A

B

C

D

E

VocabularyTerm Name Diagram Additional Notes

Concave Concave equilateral When any points of the quadrilateral lie in the exterior of the polygon.

VocabularyTerm 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.

Review of Vocabulary

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2.

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Define: Polygon

• A polygon is a plane figure that meets the following conditions:

1. It is formed by three or more segments called sides.

2. Each side intersects exactly two other sides, at each endpoint

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.

Example:

Two correct names for this polygon are:

___________ or ___________

P

Q

S

T

R

Practice!

Revisiting Names of Polygons• What did you remember?

# of sides Type of Polygon 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

Regular and Irregular Polygon

• Regular Polygon: a polygon that is both equilateral and

equiangular

• Irregular Polygon:a polygon that is not regular

Examples

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

Examples

Polygon Angle Sum Theorem

• Theorem 6 – 1 – 1

The sum of the interior angle measures of a convex polygon with n sides is

(n – 2)180°

Polygon Angle Sum Theorem Practice

a. Find the sum of the interior angle measures of a convex octagon.

Polygon Angle Sum Theorem Practice

b. Find the measure of each interior angle of a regular nonagon.

Polygon Angle Sum Theorem Practice

c. Find the measure of each interior angle of quadrilateral PQRS.

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