Download 7.1 Polygons and Exploring Interior Angles of Polygons Warm Up

7.1 Polygons and Exploring Interior Angles of Polygons
Warm Up
Given A (4,-5) and B (-2, 7) find the following:
1.Midpoint of AB
2. AB (the distance)
Evaluate each expression for n = 6.
3. (n – 4) 12
4. (n – 3) 90
Solve for a.
5. 12a + 4a + 9a = 100
7.1 Polygons and Exploring Interior Angles of Polygons
Objective: Identify, name, and describe polygons.
A polygon is a plane figure that is formed by two or more segments such that
each side intersects exactly two other sides, one at each endpoint.
Each segment of a polygon is called a side.
Any point where two sides meet is called a vertex.
(The plural of vertex is vertices.)
Two consecutive sides of a polygon form an interior angle.
You can name a polygon by listing its vertices consecutively.
For example, PQRST or QRSTP, etc.
Examples: State whether each figure is a polygon. If it is not, explain why.
1.
2.
3.
4.
Check for understanding:
Fill in the blanks below to show your understanding of the parts of a polygon.
a. Name a vertex. ____________
b. Name the polygon. ____________
c. Name a side. ____________
d. Name an interior angle. ____________
e. Name a diagonal. ____________
Polygons are also named by the number of sides they have.
Number of Sides
Type of Polygon
Number of Sides
Type of Polygon
3
Triangle
8
Octagon
4
Quadrilateral
9
Nonagon
5
Pentagon
10
Decagon
6
Hexagon
12
Dodecagon
7
Heptagon
n
n-gon
A polygon is convex if no line that contains a side of the polygon
contains a point in the interior of the polygon.
A polygon that is not convex is called nonconvex or concave.
Convex polygon
Concave polygon
Examples: Identify the type of polygon and state whether it is convex or concave.
5.
6.
7.
A polygon is equilateral if all of its sides are congruent.
A polygon is equiangular if all of its interior angles are congruent.
A polygon is regular if it is equilateral and equiangular.
Examples: Decide whether the polygon is equilateral, equiangular, regular, or neither.
8.
9.
10.
Check for understanding 2.
Draw a regular polygon. Then draw an irregular polygon with the
same number of sides.
A diagonal of a polygon is segment that joins two nonconsecutive vertices.
For example, Polygon ABCDEF has 3 diagonals from point B: BD, BE, BF.
Theorem 7.1: Sum of the Interior Angles of a Polygon
The sum of the measures of the interior angles of a polygon is equal to the
difference of the number of sides of the polygon and 2, multiplied by 180.
Sum of the interior angles = (n-2)∙180
720° = (6-2)∙180
Examples: Use the information in the diagram to solve for x.
14. What is the sum of the angles of an octagon?
15. If the figure is a regular octagon, what is the measure of each angle?