Download Geometry 4-2 Angles of Triangles

Geometry 4-2 Angles of Triangles
Theorem 4.1 - Triangle Angle Sum Theorem: The sum of
the measures of the angles in a triangle is 180.
Find the measures of each numbered angle.
B
28o 71o
A 1
3 = 180 - 57 - 71 = 52
2
o
2 = 180 - 57 = 123
57
D
1 = 180 - 28 - 123 = 29
3 C
We will prove this theorem using a different type of proof. A
flow proof
features the statements written in boxes, the
reasons beneath or beside the boxes, and arrows showing
the logical progression of the argument.
If we extend one side of a triangle, we form an exterior angle
for the triangle. The two interior angles that are not adjacent
to the exterior angle are called remote interior angles
.
exterior angle
remote interior angles
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 remote interior angles.
B
A 2
1
3 4
C
ABC
Given
Given: ABC
Prove: m 4 = m 1 + m 2
m 1 + m 2 + m 3 = 180
Triangle Angle Sum Thm
m 3 + m 4 = 180
Linear Pair = 180
m 1+m 2+m 3=m 3+m 4
Transitive
m 1 + m 2 = m 4 Subtraction
y
Find the measure of JKM.
2y - 15 = y + 50
y = 65
JKM = 2(65) - 15 = 115.
2y - 15
J
K
M
50
L
A corollary
is a theorem with a proof that follows as a
direct result of another theorem. These two corollaries
follow directly from the Triangle Angle Sum Theorem.
Corollary 4.1: The acute angles of a right triangle are
complementary.
Corollary 4.2: There can be at most one right angle or one
obtuse angle in a triangle.