Download Problem Solving Using Systems of Equations

Math 20-2
Geometry: Lesson #1
Transversals
Objective: By the end of this lesson, you should be able to:
- Generalize, using inductive reasoning, the relationships between pairs of angles
formed by transversals and parallel lines.
- Determine the measures of angles in a diagram that includes parallel lines, angles
and triangles, and justify the reasoning.
- Determine if lines are parallel, given the measure of an angle at each intersection
formed by the lines and a transversal.
E
A
s
t
u
v
B
C
w x
y z
D
F
Vocabulary

Transversal –

Interior angles –

Exterior angles –

Opposite angles –

Corresponding angles –
Math 20-2
Geometry: Lesson #1

Alternate interior angles –

Alternate exterior angles –
Key Point: There are relationships between the angles formed by parallel lines and a
transversal.
e.g. 1) Use a ruler to draw a transversal across the two parallel lines shown. (Make sure it is not
perpendicular to the lines.) Then use a protractor to measure all eight angles formed.
Make a conjecture about the following sets of angles formed by parallel lines and a
transversal:
 Corresponding angles:

Alternate interior angles:

Alternate exterior angles:

Interior angles on the same side of the transversal:

Exterior angles on the same side of the transversal:
Math 20-2
Geometry: Lesson #1
e.g. 2) The horizontal lines are parallel. Determine the measure of every indicated angle. Give
reasons for your statements.
b
c
a
112
d
e
53
e.g. 3) Are the lines shown parallel? Justify your answer.
158
23
e.g. 5) Solve for x in each of the diagrams below:
a)
3x 17
107  2x
Math 20-2
Geometry: Lesson #1
b)
x  6
5 x
Assignment:
p. 72 #2, 5
p. 79-82 #4, 20