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Triangles
A triangle is a polygon (a figure) that has three sides, three vertices,
and three angles.
A
Sides: AB, BC, CA
Angles: A, B, C,
is the symbol for triangle.
B
C
A vertex is the endpoint that joins the sides of a triangle.
Vertices: A, B, C
A triangle is named with the three vertices in any order.
ABC, BCA, or CAB
’s can be classified in two ways:
(1) by their sides and/or
(2) by their angles
Method 1: Classifying ’s by Sides
Equilateral Triangle
All sides are congruent
Scalene Triangle
No sides are congruent.
Isosceles Triangle
Two sides are congruent
Method 2: Classifying ’s by Angles
Equiangular Triangle
All angles are congruent
Obtuse Triangle
One obtuse angle (between
90o – 180o).
Acute Triangle
All angles are acute (each angle
is less than 90o)
Right Triangle
One right angle
Ex. 1
Classify the triangles by its angles and its sides. Explain.
a)
60o
60o
Equiangular Equilateral 
60o
b)
Right Isosceles 
c)
Obtuse Scalene 
120o
Open your textbooks
Pg 174 #4,6
Pg 175 # 2-10 (even)
Pg176 #12 – 22 (even)
Pg 177 #30-36 (even)
Pg178 # 42, 54, 55, 56
Exterior and Interior Angles
A
1
4
Interior Angles: 3 original angles (the
angles that are inside the triangle).
6
C
1, 2, 3 are interior angles
3
2
B
5
Exterior Angles: angles that are adjacent to
the interior angles (they form a linear pair
with the interior angles)
4, 5, 6 are exterior angles
Triangle Sum Theorem
The sum of the measures of the interior angles of a
triangle is 180o.
A
mA + mB + mC = 180o
B
C
Ex. 1 Given mA = 25o and mB = 95o, find the mC?
25 + 95 + C = 180o
A
B
 sum theorem
120+ C = 180o
C = 180 - 120
C = 60o
C
Ex. 2
A
C
Find the value of x.
B
C
+ B + A = 180o
(5x + 3)o + (47o) +(90o) = 180o
(5x + 3) + 137 = 180
5x + 3 = 180-137
5x + 3= 43
5x = 43 – 3
5x=40
x = 40/5
x=8
Find x, then find the m ∠B.
A
B
C
Ex. 3 Find the values of x and y.
To find the value of x, use GFJ
G
21o
39o
39 + 65 + x = 180 Triangle sum theorem
104 + x = 180
x = 180 - 104
x = 76o
F
65o
76oxo yo
J
HTo
find the value of y; look at FJH.
x + y = 180
76 + y = 180
y = 180 – 76
y = 104o
linear pair
Exterior Angles Theorem
The measure of an exterior angle of a triangle is equal to
the sum of the measures of the two nonadjacent interior
angles.
m1 = mA + mB
A
B
1
Ex. 4 Find each missing angle measure.
a.
m A = 40 + 30
40o
ext.  `s thm
m A = 70o
A
b.
30o
70o
113o
B
113 = m B + 70
113 – 70 = B
m B = 43o
ext.  `s thm
Ex. 5
Find the value of x.
A
=C
B
A + B = C
(6x -1) + (5x + 17) = 126
11x + 16 =126
11x = 110
X = 10
Find x.
Class Work
Pg 182 #4-14 (even)
Pg 183 #18, 20
Pg 184 #25, 2, 4, 6