Geometry 3-2 Complete Lesson: Properties of Parallel Lines

Note from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! Look at the map of streets in Clearwater, Florida. Nicholson Street and Cedar Street are parallel. Which of these pairs of angles appear to be congruent? Select all that apply.

Take Note: Summarize Postulate 3-1: The Same-Side Interior Angles Postulate. You may use the canvas to help illustrate your description.

Problem 1 Got It? If you know the measure of one of the angles, can you always find the measures of all 8 angles when two parallel lines are cut by a transversal? Explain.

You may use the canvas to help illustrate your explanation.

Take Note: Summarize Theorem 3-1: The Alternate Interior Angles Theorem. You may use the canvas to help illustrate your description.

Take Note: Summarize Theorem 3-2: The Corresponding Angles Theorem. You may use the canvas to help illustrate your description.

Problem 2 Got It? Complete the proof on the canvas. Use a color other than black for your work.

Take Note: Summarize Theorem 3-3: The Alternate Exterior Angles Theorem. You may use the canvas to help illustrate your description.

Compare and Contrast: How are the Alternate Interior Angles Theorem and the Alternate Exterior Angles Theorem Alike? How are they different?

In Problem 2, you proved that angles 1 and 8, in the diagram below, are supplementary.

What is a good name for this pair of angles? Explain.

Review Lesson 3-1: Drag each of the statements on the left into the appropriate category.

Skew lines intersect.
Parallel lines intersect.
Intersecting lines are coplanar.
Rays are parallel.
Skew lines are coplanar.

Always
Sometimes
Never

Review Lesson 2-2: Write the converse of the conditional statement and determine its truth value.

If two angles are vertical angles, then they are congruent.

Vocabulary Review: Match each symbol with its meaning.

\|\|		congruent
\cong		equivalent
=		parallel

Vocabulary Review: Classify each angle as acute, obtuse, or right.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Acute
Obtuse
Right

Use Your Vocabulary: Use the diagram to complete each sentence on the right using the correct point from the left.

The interior of the circle contains point __?__.
The exterior of the circle contains point __?__.

Use Your Vocabulary: Use the diagram to complete each sentence on the right using the correct item(s) from the left.

A
C
∠BAC
B
∠CBA
∠CAB
∠1

The vertex of ∠ABC is __?__.
Two other names for ∠ABC are __?__ and __?__. (order does not matter)

Solve It! Look at the map of streets in Clearwater, Florida. Nicholson Street and Cedar Street are parallel. Which of these pairs of angles appear to be congruent? Select all that apply.

Take Note: Summarize Postulate 3-1: The Same-Side Interior Angles Postulate. You may use the canvas to help illustrate your description.

Problem 1 Got It? If you know the measure of one of the angles, can you always find the measures of all 8 angles when two parallel lines are cut by a transversal? Explain.

You may use the canvas to help illustrate your explanation.

Take Note: Summarize Theorem 3-1: The Alternate Interior Angles Theorem. You may use the canvas to help illustrate your description.

Take Note: Summarize Theorem 3-2: The Corresponding Angles Theorem. You may use the canvas to help illustrate your description.

Problem 2 Got It? Complete the proof on the canvas. Use a color other than black for your work.

Take Note: Summarize Theorem 3-3: The Alternate Exterior Angles Theorem. You may use the canvas to help illustrate your description.

Problem 3 Got It?

Problem 3 Got It?

Problem 3 Got It?

Problem 3 Got It?

Problem 4 Got It?

Problem 4 Got It?

Compare and Contrast: How are the Alternate Interior Angles Theorem and the Alternate Exterior Angles Theorem Alike? How are they different?

In Problem 2, you proved that angles 1 and 8, in the diagram below, are supplementary.

What is a good name for this pair of angles? Explain.

Review Lesson 3-1: Drag each of the statements on the left into the appropriate category.

Review Lesson 2-2: Write the converse of the conditional statement and determine its truth value.

If two angles are vertical angles, then they are congruent.

Vocabulary Review: Match each symbol with its meaning.

Vocabulary Review: Classify each angle as acute, obtuse, or right.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Use Your Vocabulary: Use the diagram to complete each sentence on the right using the correct point from the left.

Use Your Vocabulary: Use the diagram to complete each sentence on the right using the correct item(s) from the left.

Reflection: Math Success

Geometry 3-2 Complete Lesson: Properties of Parallel Lines

Solve It! Look at the map of streets in Clearwater, Florida. Nicholson Street and Cedar Street are parallel. Which of these pairs of angles appear to be congruent? Select all that apply.

Take Note: Summarize Postulate 3-1: The Same-Side Interior Angles Postulate. You may use the canvas to help illustrate your description.

Problem 1 Got It? If you know the measure of one of the angles, can you always find the measures of all 8 angles when two parallel lines are cut by a transversal? Explain.You may use the canvas to help illustrate your explanation.

Take Note: Summarize Theorem 3-1: The Alternate Interior Angles Theorem. You may use the canvas to help illustrate your description.

Take Note: Summarize Theorem 3-2: The Corresponding Angles Theorem. You may use the canvas to help illustrate your description.

Problem 2 Got It? Complete the proof on the canvas. Use a color other than black for your work.

Take Note: Summarize Theorem 3-3: The Alternate Exterior Angles Theorem. You may use the canvas to help illustrate your description.

Problem 3 Got It?

Problem 3 Got It?

Problem 3 Got It?

Problem 3 Got It?

Problem 4 Got It?

Problem 4 Got It?

Compare and Contrast: How are the Alternate Interior Angles Theorem and the Alternate Exterior Angles Theorem Alike? How are they different?

In Problem 2, you proved that angles 1 and 8, in the diagram below, are supplementary. What is a good name for this pair of angles? Explain.

Review Lesson 3-1: Drag each of the statements on the left into the appropriate category.

Review Lesson 2-2: Write the converse of the conditional statement and determine its truth value.If two angles are vertical angles, then they are congruent.

Vocabulary Review: Match each symbol with its meaning.

Vocabulary Review: Classify each angle as acute, obtuse, or right. You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Use Your Vocabulary: Use the diagram to complete each sentence on the right using the correct point from the left.

Use Your Vocabulary: Use the diagram to complete each sentence on the right using the correct item(s) from the left.

Reflection: Math Success

Problem 1 Got It? If you know the measure of one of the angles, can you always find the measures of all 8 angles when two parallel lines are cut by a transversal? Explain.

You may use the canvas to help illustrate your explanation.

In Problem 2, you proved that angles 1 and 8, in the diagram below, are supplementary.

What is a good name for this pair of angles? Explain.

Review Lesson 2-2: Write the converse of the conditional statement and determine its truth value.

If two angles are vertical angles, then they are congruent.

Vocabulary Review: Classify each angle as acute, obtuse, or right.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.