section 3.3 triangles thompson. triangle sum theorem the sum of the measures --?--
TRANSCRIPT
Section 3.3Triangles
Thompson
Triangle Sum Theorem
The sum of the measures --?--.
The triangle angle sum theorem
• The sum of the measures of the angles of a triangle is 180.
• m<A + m<B + m<C = 180A
B C
83˚
45˚ x˚
Find the valueOf x
(4x+7)˚
(8x-1)˚
Find the valueOf x
Types of Triangles
• Equilateral– All sides congruent
• Isosceles– At least two sides are
congruent• Scalene
– No sides are congruent
“By Sides”
Page 133
Types of Triangles“By Angles”
• Equiangular– All angles are congruent
• Acute– All angles are acute (less than 90)
• Right– One right angle (90 )
• Obtuse– One obtuse angle (more than 90 less
than 180)
Classifying Triangles
Now we’re going to practice
“classifying triangles”
Both by “Sides” and by “Angles”
By Anglesequiangular
By Sidesequilateral
By Angles“Right”
By Sides“Scalene”
By Sides“Isosceles”
By Angles“Acute”
By Angles“Obtuse”
By SidesIsosceles
Definition:Exterior Angles of
Triangle• Exterior Angle– The angle formed by a side and an
extension of the side
• Remote Interior Angle– The two non-adjacent interior angles
Exterior Angle
Rem
ote
Inte
rior
Ang
les
Interior vs. Exterior AnglesAll the angles inside the triangle are
called interiorinterior angles. If you extend the sides of the triangle, then the angles that form a linear pair with the interior angles are called exteriorexterior angles.
Exterior Angle Theorem
• The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
• m<1 = m<2 + m<3
1
2
3
115˚ y˚
52˚
x˚
• The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.
• m<1 > m<2 AND m<1 > m<3
1
2
3
Corollary (free postulate)
SAT ExampleFind the
values of a, b, and c.
40
75
a
b
c
120
SAT Example
What is the value of c?
80
c
b
b
aa
“…This is pointless, when am I ever Going to run into a triangle in real life?!...”
Classwork 3.31-11 , 16-23, 31-36