Download Chapter 9: 3-D Figures Topic 1: Introduction to Polygons

Name _________________________________________
Date ________________________
Chapter 9: 3-D Figures
Topic 1: Introduction to Polygons
A Polygon is a closed figure that is formed by ______ or more coplanar line segments. The line segments are the
______________ of the polygon and the endpoints are the __________________________. Polygons are named by its vertices
starting with any vertex and going in order in either direction. Polygons are classified by their number of sides.
***Regular Polygons are both
___________________________________ and
___________________________________ ***
A Diagonal of a polygon is a ____________________________________
connecting one vertex to any other ______________________ vertex.
(When connecting the diagonals, notice that triangles are formed!)
Types of Angles:
Interior Angles: the angles inside the polygon, each angle is less than 180o
Exterior Angles: the angles formed by extending one of the two adjacent sides
***** Special Relationship: Each interior and adjacent exterior angle is supplementary
To find the measure of an angle of a given polygon we utilize the following formulas (𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑖𝑑𝑒𝑠)
Use the given information to complete the table. Round to the nearest tenth if necessary.
Example: # of Sides
Interior Sum
ONE interior
Exterior Sum
180(𝑛 − 2)
180(𝑛 − 2)
Formulas n
360
𝑛
1.)
5
2.)
18
3.)
24
ONE exterior
360
𝑛
Practice:
4.) If the measure of one exterior angle of a regular polygon is 72°, find the number of sides that the polygon has.
5.) What is the measure of an interior and an exterior angle of a regular 46-gon.
6.) If the measure of one interior angle of a regular polygon is 144°, find the number of sides that the polygon has.
7.) If the sum of the interior angles of a regular polygon is 2160°, how many sides does the polygon have?
8.) The measure of an exterior angle of a regular polygon is 2x and the measure of an interior angle is 4x.
a) use the relationship between interior and exterior angles to find the value of x.
b) Find the measure of one interior and one exterior angle.
c) Find the number of sides in the polygon.
d) what is the name of this polygon?
9.) Using the provided diagram, find the value of x.
a)
b)
c)
d)
10.) ABCDE and HIJKL are regular pentagons and AEFGHL is a regular hexagon. If <ABK ≅ <LKB, find m<ABK
Name _________________________________________
Date ________________________
Introduction to Polygons Homework
1.) Using hexagon HIJKLM
a.) Name all angles that are consecutive to < 𝐻.
_________________ and _________________
b.) Name two diagonals.
_________________ and _________________
c.) Name two consecutive sides.
_________________ and _________________
2.) If the measure of one interior angle of a regular polygon is 150°, how many sides does the polygon have?
3.) Find the measure of an interior and an exterior angle of a regular polygon who has 18 sides.
4.) If the measure of one exterior angle of a regular polygon is 24°, find the number of sides that the polygon has.
5.) If the sum of the interior angles of a regular polygon is 3060°, how many sides does the polygon have?
6.) Using the diagram find the value of x.
7.) Find the value of m.
8.) Using the regular hexagon find both x and y.
9.) Find the value of x and the measure of each angle.
10.) Find the value of x.
11.) Find the value of a, b, c, d and e.
Review Section:
12.) a.) What can be concluded about the relationship between line 𝑙 and plane P?
b.) What can be concluded about the relationship between planes P and Q?
c.) What can be concluded about the relationship between lines 𝑙 and 𝑚?
d.) What can be concluded about segments AB and CD?
e.) Line 𝑗 lies in plane P, and line 𝑖 lies in plane Q. What can be concluded about lines 𝑗 and 𝑖?
_____ 13.) The measure of the angles of a triangle are in the ratio of 2:3:4. In degrees, the measure of the
largest angle of the triangle is:
(1) 20
(2) 40
(3) 80
(4) 100