Parallel Lines and the Triangle Angle-Sum
Theorem
Geometry 12.0 – Students find and use measures of
interior and exterior angles of triangles to classify
figures and solve problems.
Geometry 13.0- Students prove relationships between
angles in polygons by using properties of
complementary, supplementary, vertical, and exterior
angles.
Triangle Investigation #2
• Is the sum of the interior angles of any triangle
180º?
– Let’s investigate!
Triangle #1
Triangle #3
Triangle #2
64º
52º
65º
59º
71º
90º
38º
57º
44º
57º + 59º + 64º =
44º + 65º + 71º =
180º
180º
38º + 52º + 90º =
180º
Triangle Investigation #3
Cut out
the triangle!
Tear off
the Angles!
Join the torn angles together!
The angles form a straight angle
180
which equals ______.
Find the value of each variable.
2)
1)
1) x= 80
70
30 40
x = 70, y = 110
z = 30
s
30
x
80
3)
x z
54
y
x y
X= 36, y = 90 , z = 38
52
z
Find the value of each variable.
e
32
d
b
c
55
a
a = 67, b= 58, c= 125,
d= 23, e = 90
Find the values of a, b, and c.
a = 70
b = 20
c = 20
Find m1.
M<1 = 35