# Geometry: Constructions Tutor

You can replace your paper, compass, and straight-edged constructions with a single app. Young geometers not only do constructions with this application, they can also watch an animated demonstration, and then test their understanding.

##### App Overview

Geometry: Constructions Tutor is a geometry app that can help bring a deeper understanding of constructions to your students. The demonstration animations can be watched over and over again for understanding, then using the built-in compass and drawing tools, they can test their understanding by building their own constructions. After completing the construction, the app checks it for accuracy.

To aid in the construction process, this app supports the following:

• Undo and redo
• Object snapping
• Magnifying glass to see detail
• Zoom in, Zoom out with finger pinch
• Detection of intersection points
• Save or e-mail completed constructions

Numerous constructions are supported including those on lines, angles, triangles, triangles and circles, circles, and regular polygons.

Lines:

• Copy a segment
• Construct a perpendicular bisector
• Divide a segment into a given number of equal parts
• Construct a perpendicular line through a point on a given line
• Construct a perpendicular line through an external point
• Construct a parallel line through a point

Angles:

• Copy an angle
• Bisect an angle
• Construct a 30 degree angle
• Construct a 45 degree angle
• Construct a 60 degree angle
• Construct a 90 degree angle

Triangles:

• Construct a triangle given three sides
• Construct a triangle given a side and two adjacent sides
• Construct a triangle given two sides and an included angle
• Copy a triangle
• Construct an equalaterial triangle
• Construct an isosceles triangle given a base and one side
• Construct an isosceles triangle given a base and an altitude
• Construct a 30-60-90 right triangle given the hypotenuse
• Construct a median in a triangle

Triangle Circles:

• Construct the incenter of a triangle
• Construct the circumcenter of a triangle
• Construct the incircle of a triangle
• Construct the circumcircle of a triangle

Circles:

• Construct the center of a circle
• Construct the tangent lines through an external point for a circle
• Construct the tangent line through a point on a circle
• Construct the circle through three given points
• Find the foci of a given ellipse

Polygons:

• Construct a hexagon given one side
• Inscribe a hexagon into a circle
• Inscribe a pentagon into a circle
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##### Instructional Ideas

Project one tablet for students with the demonstrations in a step-by-step fashion as young learners practice building their own constructions either with their own tablets or with paper, pencil, and construction tools.

##### Classroom Considerations

• Young geometers can practice their constructions over and over and watch demonstrations at their own pace.
• Students who struggle with compass constructions may find the tutorials and practice mode a more valuable option
##### Pros

• The animated demonstrations can be shown in a step-by-step fashion, or slowed down for the viewer, which allows him/her to follow at his/her own pace
##### Cons

• Users can e-mail and save constructions built through the animated demonstrations. These constructions can look identical to those built by a student, making it difficult to verify the creator of the construction