Download Angle Properties in Triangles

Math 20-2
Geometry: Lesson #3
Angle Properties in Triangles
Objective: By the end of this lesson, you should be able to:
- Prove that the sum of angles in a triangle is 180°.
- Determine the measures of angles in a diagram or contextual problem with parallel
lines, angles, and triangles.
- Identify and correct errors in a given solution to a problem involving the measure of
angles.
Key Point: The sum of all three angles in any triangle is ________°. This means if we know
the measure of two angles in a triangle, we can always find the last one.
e.g. 1) Find the missing angle in the triangle below:
109°
47°
Let’s prove that the sum of angles in a triangle is 180°. Draw a triangle ABC , with a line XY
through B and parallel to AC.
Statement
B
X
A
Y
C
Triangle Vocabulary

Equilateral triangle –

Isosceles triangle –

Scalene triangle –

Right triangle –
Reason
Math 20-2
Geometry: Lesson #3

Acute angle –

Obtuse angle –

Interior angle –

Exterior angle –

Non-adjacent interior angles –

Bisector –

Parallelogram –
e.g. 2) In the diagram, MTH is an exterior angle of MAT . Determine the measures of the
unknown angles in MAT . Give reasons for each.
M
41°
76°
A
T
H
What is the relationship between an exterior angle of a triangle and its non-adjacent interior
angles? Explain why this relationship exists.
Math 20-2
Geometry: Lesson #3
e.g. 3) In the diagram below, prove that JK
LM .
Statement
K
Reason
130°
M
45°
85°
J
L
N
e.g. 4) In the diagram below, prove that BC bisects  ACE.
E
Statement
Reason
C
B
D
A
e.g. 5) MNPQ is a parallelogram. Determine the measures of all the marked angles. Justify
your statements.
Statement
Reason
d
67º
a
39º
c
Assignment:
20º
b
Angles Worksheet