Unit 2 Resources & Lessons
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Daily Lesson Slides
Day 1: Parallel Lines & Transversals
Day 2: Angle Relationships
Day 3: Proving Lines Parallel
Day 4: Solving Problems Using Angle Relationships
Midpoint and Distance Formaula Slides
Unit 2: Complete Practice Worksheet
Unit 2: Practice Problem Worksheet
Angle Relationships: Reference Guide
Unit 2: Study Guide
Day 1: Parallel Lines & Transversals
Objective: To identify relationships between lines and planes, and to classify angles formed by a transversal.
Vocabulary
are lines on the same plane that never intersect.
A is a line that intersects two or more other lines.
are lines on different planes that never intersect.
Concept
- Lines can have different relationships:
- Parallel: Like railroad tracks, they are on the same plane and never meet.
- Skew: Like an overpass and the road below it, they are on different planes and never meet.
- When a line called a transversal cuts across other lines, it creates special angles we can study.
I Do: Examples
Example 1: Line t is the transversal because it intersects lines l and m. This creates 8 angles.
Example 2: In the cube, line AB is parallel to CD. Line AB is skew to HG.
We Do: Let's Try Together
Using the cube diagram from the "I Do" section, answer the following.
You Do: Practice On Your Own
Practice
We Do: Name a line parallel to EH: . Name a line skew to EH: .
You Do 1: In the transversal diagram, what is the special name for line t?
You Do 2: In the cube diagram, what is the relationship between lines AB and EF?
Day 2: Angle Relationships
Objective: To classify angle pairs formed by two lines and a transversal.
Vocabulary & Concept
When a transversal cuts two lines, it forms special pairs of angles with specific names based on their location.
Alternate Interior Angles: the two lines and on sides of the transversal.
Corresponding Angles: In the position at each intersection.
I Do: Examples
Example 1: In the diagram, the pair ∠4 and ∠5 are Alternate Interior Angles because they are inside lines l and m, and on opposite sides of transversal t.
Example 2: The pair ∠2 and ∠7 are Alternate Exterior Angles because they are outside lines l and m, and on opposite sides of transversal t.
We Do: Let's Try Together
Using the diagram above, classify the angle pairs.
You Do: Practice On Your Own
Using the diagram, name the angle that...
Practice
We Do: ∠2 and ∠6 are . ∠4 and ∠6 are .
You Do 1: Name the angle that forms a pair of alternate interior angles with ∠5:
You Do 2: Name the angle that forms a pair of corresponding angles with ∠3:
Day 3: Proving Lines Parallel
Objective: To use angle relationships to prove that two lines are parallel.
Vocabulary & Concept
- The Converse of a theorem is its reverse. We use these to prove lines are parallel.
- The Logic: IF special angle pairs are congruent (or supplementary), THEN the lines must be .
- The Logic: IF special angle pairs are congruent (or supplementary), THEN the lines must be .
I Do: Examples
Example 1: Given \(m\angle1 = 115^\circ\) and \(m\angle5 = 115^\circ\). Since ∠1 and ∠5 are corresponding angles and they are congruent, we can conclude that l || m by the Converse of the Corresponding Angles Postulate.
Example 2: Given \(m\angle3 = 80^\circ\) and \(m\angle6 = 80^\circ\). Since ∠3 and ∠6 are alternate interior angles and they are congruent, we can conclude that l || m by the Converse of the Alternate Interior Angles Theorem.
We Do: Let's Try Together
You Do: Practice On Your Own
Practice
We Do 1: If ∠4 ≅ ∠5, the proves the lines are parallel.
We Do 2: If m∠3 + m∠5 = 180°, the proves the lines are parallel.
You Do 1: If m∠3 = 100° and m∠5 = 80°, are the lines parallel? . Why? .
You Do 2: If ∠1 ≅ ∠8, are the lines parallel? . Why? .
Day 4: Solving Problems with Angle Relationships
Objective: To use properties of parallel lines to determine unknown angle measures.
Concept
This time, we start by knowing the lines are parallel. This allows us to make conclusions about the angles.
IF lines are parallel, THEN alternate interior/exterior and corresponding angles are .
IF lines are parallel, THEN same-side interior angles are .
I Do: Examples
Example 1: Given l || m and \(m\angle1 = 125^\circ\). Since ∠1 and ∠5 are corresponding, \(m\angle5 = 125^\circ\). Since ∠1 and ∠8 are alternate exterior, \(m\angle8 = 125^\circ\). All other angles are supplementary to 125°, so they are \(180 - 125 = 55^\circ\).
Example 2: Given l || m, \(m\angle4 = (x+20)^\circ\) and \(m\angle5 = (2x-15)^\circ\). Since they are alternate interior angles, they are equal. So, \(x+20 = 2x-15\), which means \(x=35\).
We Do: Let's Try Together
You Do: Practice On Your Own
Practice
We Do 1: Given l || m and m∠2 = 60°, what is m∠7? . Why? .
We Do 2: Given l || m and m∠3 = 110°, what is m∠5? . Why? .
You Do 1: Given l || m, m∠4 = (2x + 10)°, and m∠5 = (3x - 5)°. Find x.
You Do 2: Given l || m, m∠3 = (4x - 10)°, and m∠6 = (2x + 20)°. Find x.
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