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9-12 Geometry Unit 1 Lesson 8

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

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Unit 5
Unit 6
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Unit 8

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Lesson 8
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Lesson 10
Lesson 11
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Lesson 13
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Lesson 8

8.1 Warm-up 8.2 Activity 8.3 Activity Student Lesson Summary

Unit 1, Lesson 8

Using Technology for Constructions

Geometry

8.1

Warm-up

Open the GeoGebra Constructions Tool in the Math Tools (or at https://im612.org/construction-tool).

Familiarize yourself with your digital straightedge and compass tools by:

Drawing a few circles of different sizes.
Drawing a few line segments of different lengths.
Extending some of those line segments in both directions.

Try out any other tools you can find.

8.2

Activity

Use the GeoGebra Constructions Tool (https://im612.org/construction-tool) to create one or more of these figures:

A perpendicular bisector of line segment
An equilateral triangle
A regular hexagon

A square
A square inscribed in a circle
Two congruent, right triangles that do not share a side

In order for your construction to be successful, it has to be impossible to mess it up by dragging a point. Make sure to test your constructions.

8.3

Activity

Standards Alignment

Building On

Addressing

G-CO.12

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

View Full Standard

Building Toward

When you open the GeoGebra Geometry Tool (https://im612.org/geometry-tool), you’ll see some basic tools. Click on the word “MORE,” and you’ll see some categories of tools, including “Construct” tools.

<p>geogebra perpendicular line tool </p> — perpendicular line

<p>geogebra parallel line tool</p> — parallel line

Construct a line or a line segment and an additional point that is not on it. Then try the perpendicular line tool and the parallel line tool. Use the move tool to drag some points around, and observe what happens.
Use any of the digital tools to create one or more of these figures. Test your constructions by dragging a point.
1. parallelogram
2. rectangle
3. rhombus
4. square

Student Lesson Summary

We will start with a small set of tools. The GeoGebra Constructions Tool can be found at https://im612.org/construction-tool. These are the GeoGebra tools that do the same jobs as a pencil, a compass, and a straightedge.

Three pencil tools:

<p>geogebra point tool </p> — point

<p>geogebra point plotted on object tool </p> — point on object

<p>geogebra point of intersection of objects tool</p> — intersect

Four straightedge tools:

<p>geogebra line tool</p> — line

<p>Geogebra construct segment tool.</p> — segment

<p>Geogebra construct ray tool.</p> — ray

<p>Geogebra construct polygon tool.</p> — polygon

Two compass tools:

<p>geogebra circle with center through point tool</p> — circle with center through point

<p>geogebra compass tool</p> — compass

The GeoGebra Geometry Tool is at https://im612.org/geometry-tool. Click “MORE” to see the hidden categories of tools. Instead of doing each step of a construction, GeoGebra Geometry Tool will perform all the steps of the constructions in our inventory. It has commands for perpendicular lines, parallel lines, and more!

<p>geogebra perpendicular line tool </p> — perpendicular line

<p>geogebra parallel line tool</p> — parallel line

None

Standards Alignment

Building On

Addressing

G-CO.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

View Full Standard

Building Toward

Standards Alignment

Building On

Addressing

G-CO.12

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

View Full Standard

G-CO.13

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

View Full Standard

Building Toward