Lesson 8

Using Technology for Constructions

This lesson is optional.

In this lesson, students who haven't had the opportunity to engage with dynamic geometry technology can learn to use it to make a diagram with digital construction tools that are analogous to a compass and straightedge. Students review constructions they have done on paper and build toward more complex constructions made easier by technology. The work of this lesson connects to upcoming work because students will have the opportunity to use this technology throughout the course. The activity Digital Compass and Straightedge Construction is left open and unstructured intentionally so students have the opportunity to make sense of problems (MP1).

Encourage students who finish an activity early to play, make a composite figure, or recreate a design from a previous lesson.

Coordinate (orally) technology tools with paper and pencil tools to construct a diagram.

Let’s use technology to construct a diagram.

Dynamic geometry software

Acquire devices that can run GeoGebra (recommended) or other dynamic geometry technology. It is ideal if each pair of students has a device. (The GeoGebra Construction App and Geometry App are available under Math Tools.)

I can use technology to help me construct specific diagrams.

Addressing

angle bisector

A line through the vertex of an angle that divides it into two equal angles.
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 \(O\).
conjecture

A reasonable guess that you are trying to either prove or disprove.
inscribed

We say a polygon is inscribed in a circle if it fits inside the circle and every vertex of the polygon is on the circle. We say a circle is inscribed in a polygon if it fits inside the polygon and every side of the polygon is tangent to the circle.
line segment

A set of points on a line with two endpoints.
parallel

Two lines that don't intersect are called parallel. We can also call segments parallel if they extend into parallel lines.
perpendicular bisector

The perpendicular bisector of a segment is a line through the midpoint of the segment that is perpendicular to it.
regular polygon

A polygon where all of the sides are congruent and all the angles are congruent.