journal prompt – “let’s reflect”

Journal Prompt – “Let’s Reflect”

We are now starting our third unit in this class. We’ve taken several quizzes and two unit tests. By this point, you should start to have an idea of what is working and what is not working for you in this class.

Write me a letter about how your feel about this class.Consider the following..

What are you doing in class that is working/not working?What are you doing at home that is working/not working?What is Mr. Koberstein doing during class that is

working/not working?What are you going to do differently this unit to improve

your grade?

Unit 3 – Parallel Lines and Polygons

Essential Questions:How can we use deductive reasoning to

make conclusions about parallel lines?

How can we use properties of parallel lines to solve problems about the angles of polygons?

Bonus Question A carpenter builds a stairway by cutting triangles like ∆ABC and ∆CDE from a

piece of lumber as shown below.

∠DCE and ∠FEG are corresponding angles relative to what pair of parallel segments and what transversal? Name another set of corresponding angles and their related parallel segments and transversal. Explain why ∠HGI and ∠GIH are not same-side interior angles. Which angle would be same-side interior to ∠HGI? If the carpenter knows that ∠KIJ as a measure of 47°, what is the measure of ∠ACB?

3-1 Properties of Parallel Lines

ObjectivesTo identify angles formed by two lines and

a transversalTo prove and use properties of parallel lines

TransversalDefinition: A transversal is a line that

intersects two coplanar lines at two distinct points.

TransversalA transversal forms eight angles. The diagram

below shows the eight angles formed by a transversal t and two lines l and m.

Special AnglesPairs of the eight angles have special names as suggested by their positions

More Pairs

Identifying Angles

Alternative Angles:

Same-Side Angles:

Corresponding Angles:

Properties of Parallel Lines In the photograph, the vapor trail of the high-flying

aircraft suggests a transversal of the parallel trails of the low-flying aircraft.

What do you notice about the measures of the angles formed?

Let’s look at a pair of parallel lines cut by a transversal.

What kind of angles are 1 and 2?

If we TRANSLATE the bottom line upward, what do we notice?

1

2

Properties of Parallel Lines

I.

Let’s look further…Suppose mb = 60

Use what you know about vertical, supplementary, and corresponding angles to find the measures of all the other angles

Can we make any conclusions?

More Postulates

When a transversal intersects two parallel lines, we have two other interesting angle properties

II.

III.

Using a two-column proofYou can display the steps that prove a theorem

in a two-column proof

Use a two-column proof to prove Alt. Int. Angles are Congruent

Statement Reasons

Classwork and HomeworkClasswork

Lesson 3-1 Practice (whole page)

Homework Practice 3-1 (half page)