Download Warm-Up Exercises

Bell Work
• Summarize your mistakes into five main things you did wrong or
topics you did not understand during the Chapter 7 Test. List them.
• What are three things you could have done differently to study for
the Chapter 7 Test.
• Set a goal for Chapter 8.
Introduction to Chapter 8
• An n-gon is a polygon with n sides and n vertices.
• Use a straightedge to draw convex polygons with the following
number of sides
•
•
•
•
3
4
5
6
• In each polygon draw all the diagonals from one vertex.
• A diagonal is a segment that joins two nonconsecutive vertices.
Introduction to Chapter 8
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Number of Sides
3
Number of
Triangles
1
Sum of Measures
of Interior Angles
180°
Introduction to Chapter 8
• Look for a pattern in the last column of your table.
• What would the sum of measures of the interior angles of a convex
heptagon be? Convex octagon?
• Write a rule for the sum of the measures of the interior angles in a
convex n-gon.
• Would the sum of the interior angles change if we changed the side
lengths?
Warm-Up
Exercises
Notes
Theorems
Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n-gon is
(n – 2)180°
Interior Angles of a Quadrilateral
The sum of the measures of the interior angles of a quadrilateral is
______.
Warm-Up1Exercises
EXAMPLE
Find the sum of angle measures in a polygon
Find the sum of the measures
of the interior angles of a
convex octagon.
Warm-Up2Exercises
EXAMPLE
Find the number of sides of a polygon
The sum of the measures of the interior angles of a
convex polygon is 900°. Classify the polygon by the
number of sides.
Warm-Up
Exercises
GUIDED
PRACTICE
1. The coin shown is in the
shape of a regular 11- gon.
Find the sum of the measures
of the interior angles.
2. The sum of the measures of the interior angles of
a convex polygon is 1440°. Classify the polygon
by the number of sides.
Warm-Up3Exercises
EXAMPLE
Find an unknown interior angle measure
ALGEBRA Find the value of x in the diagram shown.
Warm-Up
Exercises
GUIDED
PRACTICE
3. Use the diagram at the right.
Find m S and m T.
4. The measures of three of the interior angles of a
quadrilateral are 89°, 110°, and 46°. Find the
measure of the fourth interior angle.
Warm-Up
Exercises
Notes
Theorems
Polygon Exterior Angles Theorem
http://www.geogebratube.com/student/m123612
http://www.geogebratube.com/student/m144946
http://www.geogebratube.com/student/m36302
The sum of the measure of the exterior angles of a convex polygon,
one angle at each vertex, is ______.
Warm-Up4Exercises
EXAMPLE
Warm-Up
Exercises
GUIDED
PRACTICE
5. A convex hexagon has exterior angles with
measures 34°, 49°, 58°, 67°, and 75°. What is the
measure of an exterior angle at the sixth vertex?
Warm-Up5Exercises
EXAMPLE
The trampoline shown is shaped like a regular
dodecagon. Find (a) the measure of each interior
angle and (b) the measure of each exterior angle.
Warm-Up
Exercises
Daily
Homework
Quick
CheckQuiz
1.
Find the sum of the measures of the interior angles
of a convex 24-gon.
2.
The sum of the measures of the interior angles of
a convex polygon is 5040o. Classify the polygon by
the number of sides.
Warm-Up
Exercises
Daily
Homework
Quick
CheckQuiz
3.
Find the value of x.
4.
Find the measures of an interior angle and an
exterior angle of a regular 36-gon.
Warm-Up
Exercises
For Tomorrow
Homework
HW: 8.1 (pg. 504-506) #1,4,8,12,17,24,25,28