Linear AlgebraProblem 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. Angles 1 and 3 are congruent because_______________________________________.2. Angles 5 and 7 are congruent because_______________________________________.3. What transformation “moves” angle 5 exactly onto angle 1? Explain.4. 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.4. 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.4. 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 DYES 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 DAngle BCA is the alternate interior angle to angle 3 so they are congruent.

1 3

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