Lesson 1

Build It

This lesson establishes the straightedge and compass moves that students will use to perform various constructions. Students build on their previous understanding of circles as a set of points all equidistant from the center and line segments as a set of points on a line with two endpoints. Constructions are used in subsequent lessons to introduce students to reasoning about distances, generating conjectures, and attending to the level of precision required to define rigid motions later in the unit.

Students attend to precision when they discuss why straightedge and compass moves communicate geometric information consistently, as opposed to eyeballing (MP6).

These materials use words rather than symbolic notation to allow students to focus on the content. By using words, students do not need to translate the meaning of the symbol while reading. To increase exposure to different notations, images with given information marked using ticks, right angle marks, or arrows also have a caption with the symbolic notation (\(\overline{AB} \cong \overline{AC}, \overline{AB} \perp \overline{AC}\) or \(\overline{AB} \parallel \overline{AC}\)). Feel free to use the symbolic notation when recording student responses, as that is an appropriate use of shorthand.

In this lesson and the subsequent lessons in this section, all constructions are accessible using physical straightedges and rigid compasses. If students have ready access to digital materials in class, they can choose to perform any or all construction activities with the GeoGebra Construction tool accessible in the Math Tools or available at geogebra.org/m/VQ57WNyR. The warm-up of the optional lesson "Using Technology for Constructions" is a good primer for the GeoGebra Construction tool. Do that warm-up with students before starting this lesson if students will use the digital tool rather than physical tools. If students do not have ready access to this digital tool in class, consider using the GeoGebra Construction tool to demonstrate constructions during the activity or lesson syntheses.

Comprehend that compasses create circles and can be used to transfer distances across a construction.
Create diagrams using a straightedge to produce a line or segment through two points.

Let’s use tools to create shapes precisely.

Geometry toolkits (HS)

Create a display of straightedge and compass moves that will remain displayed for all to see throughout the unit. See the warm-up synthesis for an example.

Assemble geometry toolkits. It would be best if students had access to these toolkits at all times throughout the unit.

I can create diagrams using a straightedge.
I know to use a compass to construct a circle.

Addressing

Building Towards

circle

A circle of radius \(r\) with center \(O\) is the set of all points that are a distance \(r\) units from \(O\).

To draw a circle of radius 3 and center \(O\), use a compass to draw all the points at a distance 3 from \(O\).
line segment

A set of points on a line with two endpoints.