Basic Constructions

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Objective

SWBAT perform the following constructions and informally explain why they work: Copy a segment; Bisect a segment; Copy an angle; Bisect an angle; SWBAT use measurement to verify constructions

Big Idea

We're Under Construction....and not sorry about it. In this lesson students use a compass and straightedge to perform basic geometric constructions and explain why they work.

Activating Prior Knowledge

15 minutes

Where We've Been: Students have learned to use correct geometric naming conventions, symbolic notation, and diagrams. They also know and understand basic geometric terminology.

Where We're Going: We're introducing geometric constructions for the first time in the course.

 

The goal of this section is to make sure that students have a solid understanding of the figures they will be constructing: congruent segments, congruent angles, segment bisector, and angle bisector.

 

To help with achieving this goal, I use the Activating Prior Knowledge: Basic Constructions resource. As students are working, I walk around doing some informal assessment. I give feedback to get students to be precise with their diagrams (e.g., using tick marks appropriately).

Concept Development

15 minutes

Since this is our first time doing constructions, I have to introduce some fundamental concepts. So I give students the following notes: 

Classic Geometric Construction: A method of creating geometric figures using only a compass and a straightedge.

Compass: A compass is a tool for making circles or arcs with a specific radius.

Straightedge: An object with a straight edge that is used only to make straight segments (i.e., it is not used as a measurement device)

Circle: The locus of points in a plane that are equidistant from a point called the center

Radius: The distance between the center of a circle and any point on the circle

Arc: A continuous part of a circle

locus: The set of all points satisfying a given condition

 

So a compass creates a set of points (an arc or circle) that are equidistant from the center of a circle. The center of the circle is marked by the sharp point of the compass. We set the radius of the compass to determine the distance from the center that all of the points will be.

Keep in mind when we are doing constructions that this is what the compass is doing.

Guided Practice

60 minutes

For this section of the lesson, all students have a compass and straightedge. I also give each student four sheets of blank white copy paper.

For starters, I show students how to adjust the radius of the compass. We start with a radius of 2.5 cm. Then I ask them to draw a circles with radius 2.5 cm. Then I walk around to make sure that no one is having major compass complications.

 

Next I instruct students to give one of the sheets of white paper the heading "Construction: Copying a Segment"

I run the copying a segment demonstration several times so that students get a feel for it. Then I show the demonstration one step at a time so that students can perform the construction themselves. Next, I have students write down the steps of the construction and a short explanation of why it works. Finally, I have students to verify that the segments are congruent. If they are congruent, students should mark the diagram appropriately ( with the lengths and with tick marks).

 

We then repeat this same process for bisecting a line segment, copying an angle, and bisecting an angle.

Independent Practice

The resource Independent Practice: Basic Construction are the worksheets from mathopenref.com that were designed to accompany the construction demonstrations. I use these as independent practice on the day following this lesson.