Geo 3.4 Triangle Theorems.notebook
October 16, 2015
Triangle Inequality Theorem:
the sum of 2 sides is always greater than the 3rd side
3.4 Triangle Theorems
B
I CAN...
Apply the Triangle Inequality Theorem
Apply side­angle relationships in triangles
Apply the Triangle Angle­Sum Theorem and Exterior Angle Theorem
12
6
A
Jul 24­9:36 AM
C
9
Jul 24­9:36 AM
Is it a triangle given the 3 side measures?
3, 4, 5
6 + 9 > 12
12 + 9 > 6
12 + 6 > 9
Given two sides of a triangle are 11 and 15, what is the range of the third side?
2, 4, 8
6, 6, 12
___ < x < ___
difference of 2 sides
Jul 24­9:36 AM
Jul 24­9:36 AM
Given 2 sides, what is the range for the measure of the 3rd side?
5 and 9
___ < x < ___
sum
of 2 sides
4 and 7
___ < x < ___
Side & Angle Relationships
B
What is the biggest angle?
50
100
30
So what is the biggest side then?
C
A
What is the smallest angle?
So what is the smallest side then?
Jul 24­9:36 AM
Jul 24­9:36 AM
1
Geo 3.4 Triangle Theorems.notebook
Triangle Angle­Sum Theorem
m ∠ A + m ∠ B + m ∠ C = 180
October 16, 2015
Triangle Angle­Sum Theorem Proof
B
D
Given: AC DB
Prove: m∠1 + m∠2 + m∠3 = 180.
B
4
3
5
2
1
C
A
Reasons
Statements
C
A
1. 2. m∠4 + m∠3 + m∠5 = 180.
3. m∠1 = m∠4
4. m∠2 = m∠5
5. Jul 24­9:36 AM
Find the measure of each numbered angle.
Jul 24­9:36 AM
An Exterior Angle is...
An angle formed by one side of a triangle and the extension of another side.
Remote Interior Angles are...
The angles of a triangle that are not adjacent to a given exterior angle.
Exterior Angle
3
Remote Interior
Angles
2
Jul 24­9:36 AM
Exterior Angle Theorem
(Remote Angle Theorem)
m∠A + m∠B = m∠1
B
1
Jul 24­9:36 AM
Exterior Angle Theorem Proof
B
Given: ΔABC
Prove: m∠Α + m∠Β = m∠1
2
Statements
1
A
C
Jul 24­9:36 AM
A
1
C
Reasons
1. 2. m∠Α + m∠Β + m∠2 = 180°
3. m∠1 + m∠2 = 180°
4. m∠Α + m∠Β + m∠2 = m∠1 + m∠2
5. m∠Α + m∠Β = m∠1
Jul 24­9:36 AM
2
Geo 3.4 Triangle Theorems.notebook
October 16, 2015
Find the measure of ∠FLW.
Find the measure of ∠ACD.
Jul 24­9:36 AM
Jul 24­9:36 AM
Triangle Angle­Sum Theorem Corollary
1. The acute angles of a right triangle are complementary
A
m∠A + m∠B = 90
C
B
2. There can be at most one right or obtuse angle in a triangle.
Jul 24­9:36 AM
3