1. Triangles

2. is the symbol for triangle.
A triangle is a polygon (a figure) that has three sides, three vertices, and three angles. A vertex is the endpoint that joins the sides of a triangle.
Sides: AB, BC, CA A
Angles: A, B, C,
is the symbol for triangle. B C
Vertices: A, B, C
A triangle is named with the three vertices in any order.
A triangle is named with the three vertices in any order.
ABC, BCA, or CAB

3. ’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
Isosceles Triangle
Scalene Triangle
All sides are congruent
Two sides are congruent
No sides are congruent.

4. Method 2: Classifying ’s by Angles Equiangular Triangle
Acute Triangle
Obtuse Triangle
Right Triangle
All angles are acute (each angle is less than 90o)
All angles are congruent
One obtuse angle (between 90o – 180o).
One right angle

5. Equiangular Equilateral 
Ex. 1 Classify the triangles by its angles and its sides. Explain. a) b)
60o
Equiangular Equilateral 
60o
60o
Right Isosceles 

6. c)
Obtuse Scalene 
120o

7. 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

8. Exterior and Interior Angles
Interior Angles: 3 original angles (the angles that are inside the triangle). 4 1 6 3
1, 2, 3 are interior angles C
Exterior Angles: angles that are adjacent to the interior angles (they form a linear pair with the interior angles) 2 5 B
4, 5, 6 are exterior angles

9. Triangle Sum Theorem mA + mB + mC = 180o
The sum of the measures of the interior angles of a triangle is 180o. A
mA + mB + mC = 180o B C

10. 25 + 95 + C = 180o  sum theorem 120+ C = 180o C = 180 - 120
Ex. 1 Given mA = 25o and mB = 95o, find the mC?
C = 180o  sum theorem
120+ C = 180o A B
C =
C = 60o C

11. Ex. 2 Find the value of x.
C B A = 180o
(5x + 3)o + (47o) +(90o) = 180o
A B C
(5x + 3) = 180
5x + 3 =
5x + 3= 43
5x = 43 – 3
5x=40
x = 40/5
x = 8

12. Find x, then find the m ∠B. A B C

13. 39 + 65 + x = 180 Triangle sum theorem 104 + x = 180
Ex. 3 Find the values of x and y.
To find the value of x, use GFJ G
21o
x = Triangle sum theorem
39o
104 + x = 180
x =
x = 76o
65o
76o xo yo
To find the value of y; look at FJH. F H J
x + y = 180 linear pair
76 + y = 180
y = 180 – 76
y = 104o

14. 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

15. Ex. 4 Find each missing angle measure.b.
m A = ext.  `s thm
40o
m A = 70o A
30o
113 = m B ext.  `s thm
70o
113o
113 – 70 = B
m B = 43o B

16. A + B = C (6x -1) + (5x + 17) = 126 11x + 16 =126 11x = 110 X = 10
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

17. Find x.

18. Class Work
Pg 182 #4-14 (even) Pg 183 #18, 20 Pg 184 #25, 2, 4, 6