CH. 4.1
APPLY
TRIANGLE SUM
PROPERTIES
VOCAB
Interior Angles:
angles inside the triangle (sum = 180)
exterior
angle
Interior
angles
exterior
angle
Exterior Angles:
angles outside the triangle
exterior
angle
CLASSIFYING BY SIDES
SCALENE
_____ CONGRUENT
SIDES
ISOSCELES
_____ CONGRUENT
SIDES
EQUILATERAL
_____ CONGRUENT
SIDES
CLASSIFYING BY SIDES
SCALENE
0 CONGRUENT
____
SIDES
ISOSCELES
2 CONGRUENT
_____
SIDES
EQUILATERAL
3 CONGRUENT
_____
SIDES
CLASSIFYING BY ANGLES
ACUTE
_____ ACUTE
ANGLES
RIGHT
_____ ACUTE
ANGLES
OBTUSE
_____ ACUTE
ANGLES
EQUIANGULAR
_____ ACUTE
ANGLES
CLASSIFYING BY ANGLES
ACUTE
3 ACUTE
_____
ANGLES
RIGHT
2
_____ ACUTE
ANGLES
OBTUSE
2
_____ ACUTE
ANGLES
EQUIANGULAR
3
_____ ACUTE
ANGLES
THEOREM 4.1: TRIANGLE SUM THEOREM
The sum of the measures of the interior angles of a triangle is ________.
B
A
C
m<A + m<B + m<C = ______
THEOREM 4.1: TRIANGLE SUM THEOREM
180
The sum of the measures of the interior angles of a triangle is ________.
B
A
C
180
m<A + m<B + m<C = ______
THEOREM 4.1: TRIANGLE SUM THEOREM
EX.
B
71
A
42
x
C
m<A + m<B + m<C = 180
THEOREM 4.1: TRIANGLE SUM THEOREM
EX.
B
71
A
42
x
C
m<A + m<B + m<C = 180
42 + 71 + x = 180
113 + x = 180
- 113
- 113
x = 67
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 ________ ANGLES.
B
A
1
C
m<1 = m<__ + m<__
THEOREM 4.2: EXTERIOR ANGLE THEOREM
The MEASURE OF AN EXTERIOR ANGLE OF A TRIANGLE IS EQUAL TO THE SUM
nonadjacent ANGLES.
OF THE MEASURES OF THE TWO __________________
B
A
1
C
B
A + m<__
m<1 = m<__
THEOREM 4.2: EXTERIOR ANGLE THEOREM
EX.
B
71
A
42
1
C
m<1 = m<A + m<B
THEOREM 4.2: EXTERIOR ANGLE THEOREM
EX.
B
71
A
42
1
C
m<1 = m<A + m<B
m<1 = 42 + 71
m<1 = 113
EXAMPLE 3
B
73
3x - 9
D
C
m<1 = m<A + m<B
x
A
EXAMPLE 3
B
73
3x - 9
D
C
x
A
m<1 = m<A + m<B
3x – 9 = x + 73
 move small x to big x
-x
-x
2x – 9 = 73
 solve for x
+9 +9
3x–9=
2x = 82
x = 41 so, 3(41) – 9 = 114
2
2
COROLLARY TO THE TRIANGLE SUM THEOREM
THE ACUTE ANGLES OF A RIGHT TRIANGLE ARE ____________________.
C
A
B
m<A + m<B = ______
COROLLARY TO THE TRIANGLE SUM THEOREM
COMPLEMENTARY
THE ACUTE ANGLES OF A RIGHT TRIANGLE ARE ____________________.
= 90
C
A
B
90
m<A + m<B = ______
COROLLARY TO THE TRIANGLE SUM THEOREM
EX.
C
A
27
x
B
m<A + m<B = 90
COROLLARY TO THE TRIANGLE SUM THEOREM
EX.
C
A
27
x
B
m<A + m<B = 90
27 + x = 90
- 27
- 27
x = 63