Download 4-1 Geometry


Bellwork
Classify each angle as acute, obtuse or right




90o
72o
116o
How do we know that angle 1 and angle 2 are congruent?
1
2
Apply Triangle Sum
Properties
Section 4.1
The Concept



Today we’re going to recover some of the basics of triangles
For most this should be review of some topics learned earlier in
middle school
The terminology used today will continue to be used throughout our
study of triangles
Triangle Definition
There are two ways to describe triangles, by sides and by angles
Definitions by side:
 Scalene: No sides are of equal lengths

Isosceles: Two sides are of equal lengths

Equilateral: All sides are of equal lengths
Triangle Definition
Definitions by angles:
 Acute: Containing three acute angles

Right: Containing one right angle

Obtuse: Containing one obtuse angle

Equiangular: Containing three acute congruent angles
Examples
Classify these angles by both sides and angles
Definitions
Two important definitions for us in regards to triangles are:
 Interior Angles


Exterior Angles


Angles inside the triangle
Angles formed by extending the sides of a triangle
Important fact:

An interior and it’s matching exterior angle form a linear pair
Activity
You are now getting a piece of paper, ruler and a triangle
1.
Trace your triangle on the piece of paper
2.
On you paper, draw a straight line that does not touch or
intersect your triangle
What does this
3.
Sit quietly & patiently until everyone’s ready…
tell us about
the sum of the
angles in a
triangle?
Theorems
Theorem 4.1: Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180o
Activity
Let’s do another activity with our triangles
1.
Draw an exterior angle off of one of the corners of your traced
triangle
2.
Take the interior angle out of your torn pieces
3.
Line the two angles up in the space provided What does this tell
us about the sum of
the other two angles
in a triangle with
relation to the third?
Theorems
Theorem 4.1: Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180o
Theorem 4.2: Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of
the measures of the two non-adjacent interior angles
Corollary to Triangle sum Theorem
The acute angles of a right triangle are complementary
Examples
Find the values of the angles

80
e
70
c
d
a
b
25
80
Homework

4.1

1-7, 8-26 even, 27-34, 40-52, 55, 58, 62
Most Important Points



Different kinds of Triangles by sides & angles
Triangle Sum Theorem
Exterior Angle Theorem