Download 7-9 Triangle-Sum Property

6-8 The Triangle-Sum Property
Objective:
1.
2.
use the triangle-sum property to find measures of given angles
explain the consequences of the triangle-sum property
Big Idea: In any triangle, the sum of the measures of the three angles is 180
Triangle-Sum Property – In any triangle, the sum of the measures of the angles is 180.
Deductive Reasoning – (deduction) means that you reason logically from some things that you
know are true or assume to be true.
Finding the measure of a 3rd angle of a triangle.
69
47
x
47 + 69 +x = 180
116 + x = 180
116 + -116 + x = 180 + -116
x = 64
Check: 47 + 69 + 64 = 180
180 = 180
Angle exterior to a triangle – an angle that is outside a triangle, made by extending one of the
sides of the triangle. It is a linear pair with the interior (inside) angle of the triangle.
Finding the measure of an angle exterior to a triangle
Angle
exterior
to Δ
31
62
y
First find y, the inside angle
62 + 31 + y = 180
93 + y = 180
93 + -93 + y = 180 + -93
y = 87
x
Then find x by using linear pair relationship with y
87 + x = 180
87 + -87 + x = 180 + -87
x = 93
Finding the measures of angles given triangles and parallel lines.
4 = 68
so 2 = 68
by alt. interior 
68
10
9
7
8
11
4 1
5
2
6 3
1 +  2 + 90 = 180
1 + 68 + 90 = 180
1 + 158 = 180
1 + 158 + -158 = 180 + -158
1 = 22
Find all the measures of ’s v, w, x, y, z
Extend the lines to see
parallel line angle
relationships.
C
B
X
A
V
Y
36º
W
119º
E
mV = 83º
Z
D
mW = 61º because it’s a linear pair with  BED
mW =61º
mX =83º
mY =97º
mZ =61º
mX – use triangle sum theorem with A and BEA
36º + 61º + X = 180º
-97 + 97 + X = 180 + -97
X = 83º
mY = 97º because it is a linear pair with EBA
mZ = 61º because it is a corresponding angle with AEB
mV = 83º because it is a corresponding angle with ABE