## Constructions Problems - Section 4: Constructions Problems

*Constructions Problems*

*Constructions Problems*

# Use Constructions to Show Slope Criteria for Parallel and Perpendicular Lines

Lesson 6 of 11

## Objective: Students will be able to show the slope criteria for parallel and perpendicular lines by construction.

#### Warm-Up: Origamics Problem

*15 min*

In the Origamics Problem, students follow directions to fold their square paper to unearth important angle relationships. This problem provides students with a hands-on way to physically show angle relationships, as well as multiple ways to justify one's reasoning for how to find the measure of all angles.

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To review constructing perpendicular and parallel lines in a coordinate geometry context, I have my students:

- Graph a line segment
- Perpendicularly bisect it
- Construct a perpendicular through a point to the line segment

Through this exercise my students use geometry ideas to deepen their conceptual understanding of why lines that are parallel have equal slopes and why lines that are perpendicular have slopes that are negative reciprocals of each other.

Afterward, a whole-class discussion provides an opportunity for me to preview how we will prove the slope criteria for parallel and perpendicular lines, which we will do later on the year when we get to the unit on Triangle Similarity.

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#### Constructions Problems

*20 min*

This in-class asks students to use their constructions skills to successfully complete four constructions problems. As I launch this task, I ask my students to first sketch and label the figure they have been asked to construct -- this is important because students sometimes begin their constructions without an idea of what their construction should ultimately look like. Making a sketch sparks gives them a perspective on the problem from which to imagine a plan of attack. I tell my students to first create an image and a plan, then construct the figure using a compass and straightedge. Afterward, describe the steps of your construction in a few short sentences.

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I give this Constructions Review Homework because it asks students to review foundational constructions, which are essential as we near the end of this unit. I ask students to reflect on their level of understanding when we correct this homework in class, which often gives students an idea of their level of success with constructions.

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Introducing Constructions: Copy a Segment and Angle
- LESSON 2: Bisect Segments and Construct Perpendiculars
- LESSON 3: Tri-Mind: Perpendiculars and Squares
- LESSON 4: Bisect Angles
- LESSON 5: Construct Parallel Lines Through a Point Not on the Line
- LESSON 6: Use Constructions to Show Slope Criteria for Parallel and Perpendicular Lines
- LESSON 7: Construct Points of Concurrency
- LESSON 8: Constructions Teaching Project: Day 1 of 3
- LESSON 9: Constructions Teaching Project: Day 2 of 3
- LESSON 10: Constructions Teaching Project: Day 3 of 3
- LESSON 11: Constructions Unit Assessment