# Geometry Fall 2011 Lesson 35 _Exterior angle of a triangle_sum of interior and exterior angles of a polygon_

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Lesson Plan #35
Class: Geometry                                                                         Date: Monday November 21st, 2011

Topic: Exterior angle of a triangle

Aim: What is the relationship between the exterior angle of a triangle and the 2 remote interior angles of the triangle?

Objectives:                                            HW #35:
1) Students will know the relationship between
an exterior angle of a triangle and the 2
remote interior angles of the triangle.

Do Now:
1) What is it called when two simple statements
are joined with the word and?
A) Disjunction        B) negation
C) Biconditional      D) conjunction

2)

PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance                               Assignment #1: Complete the proof below
Give Back HW                                  Given:       with exterior       at vertex
Collect HW                                    Two non-adjacent interior angles    and
Go over the Do Now                            Prove: 6.

Statements                                                            Reasons
1.        with exterior          at vertex                  1.
2         and           form a linear pair                  2. A linear pair of angles are two angles whose sum is a straight angle.
3.
4.                                                          4.
5.                                                          5.
6.                                                          6.

Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the
2

Online Interactive Activity : Let’s go http://www.mathopenref.com/triangleextangle.html and see the relationship
between an exterior angle of a triangle and the two remote interior angles.

Assignment #1:

Find

Assignment #2:
If the measure of the exterior angle = (3x - 10) degrees and the measure of the two remote
interiors angles are 25 degrees and
(x + 15) degrees, find x.

Assignment #4: Find the values of    and   in the diagram at right.

Assignment #5:

Assignment #6:
3
Notice each of the interior angles of the polygons at right
measures less than 180o. These are known as convex polygons.

If the polygon has at least one angle measuring more than 180 o, it
is called a concave polygon.

Question:

What do we call a polygon whose sides are all the same length
and whose angles are all the same measure?

Online Interactive Activity : Let’s see regular polygons in action. Let’s go to
http://www.mathopenref.com/polygonregular.html

So we stated that the sum of the angles of a triangle is 180 o and the sum of the angles of a
quadrilateral is 360o. Let’s see how we can find the sum of the angles of a pentagon, then try to
generalize a formula for the sum of the interior angles of a polygon of n sides. Examine the
pentagon below. To help you discover the formula, see how many non-overlapping triangles you
can create, then use this to come up with a sum of the angles of a pentagon.

Try it for a six sided figure (hexagon).

What is the formula for the sum of the interior angles of a polygon with n sides?

Online Interactive Activity : Let’s check out the sum of the interior angles of a polygon
in action. Let’s go to http://www.mathopenref.com/polygoninteriorangles.html

Online Interactive Activity Let’s check out the sum of the exterior angles of a polygon, taking one exterior angle at
each vertex.
http://www.mathopenref.com/polygonexteriorangles.html

What is the formula for the sum of the exterior angles of any polygon of n sides, taking one exterior angle at each vertex?
4
5

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