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Linear Algebra
Problem 3.4
Monday, September 8
Problem 3.4 answers
Problem 3.4 ACE answers #10
Learning Target
I will understand two important geometric
properties – that parallel lines cut by a
transversal form various pairs of congruent
angles and that the angle sum of any triangle is
180o.
3.5 Parallel Lines, Transversals and
Angle Sums Important Properties
Consider the image below.
Lines m and n are parallel and are
cut by a transversal – line t.
What can you say about the
angles that are formed?
3.5 Parallel Lines, Transversals and
Angle Sums
In any triangle, what is the sum of
measures of the interior angles?
It is always equal to 180o which is
equal to a straight angle.
Problem 3.5 A
Complete the following
sentences to explain why
angles 1, 3, 5 and 7 are
congruent.
1.
2.
3.
4.
Angles 1 and 3 are congruent because_______________________________________.
Angles 5 and 7 are congruent because_______________________________________.
What transformation “moves” angle 5 exactly onto angle 1? Explain.
Are angles 1, 3, 5, and 7 all congruent? Explain.
Problem 3.5 A
Complete the following
sentences to explain why
angles 1, 3, 5 and 7 are
congruent.
1. Angles 1 and 3 are congruent because angles 1 and 3 are opposite or vertical angles.
2. Angles 5 and 7 are congruent because angles 5 and 7 are opposite or vertical angles.
3. What transformation “moves” angle 5 exactly onto angle 1? Explain.
You can translate angle 5 onto angle 1 by sliding line n along line t to match with line m.
2. Are angles 1, 3, 5, and 7 all congruent? Explain.
Problem 3.5 B
Construct an argument of
your own to show that angles
2, 4, 6 and 8 are congruent.
1. Angles 1 and 3 are congruent because angles 1 and 3 are opposite or vertical angles.
2. Angles 5 and 7 are congruent because angles 5 and 7 are opposite or vertical angles.
3. What transformation “moves” angle 5 exactly onto angle 1? Explain.
You can translate angle 5 onto angle 1 by sliding line n along line t to match with line m.
2. Are angles 1, 3, 5, and 7 all congruent? Explain.
Problem 3.5 B Answer
Problem 3.5 C
Problem 3.5 C Answer
Problem 3.5 D
YES It’s true. If all interior angles for
the blue triangle were 60o, then the
supplementary angles have to be
120o.
Problem 3.5 D
Angle BAC is the
alternate interior angle
to angle 1 so they are
congruent
1
Problem 3.5 D
1 3
Angle BCA is the
alternate interior
angle to angle 3
so they are
congruent.
Rate Your Learning
I will understand two important geometric
properties:
• that parallel lines cut by a transversal form
various pairs of congruent angles and
• that the angle sum of any triangle is 180o.
Homework for Problem 3.5
ACE p. 61 #11-13