Investigating Geometry with GeoGebra

Henrico County Public Schools

Construct a triangle given two sides and an angle.

READ the instructions on the right and INTERACT with the GeoGebra applet below.

Sorry, the GeoGebra Applet could not be started. Please install Java 1.4 (or later) to use this page.

Given three sides 4, 6 and 8.

Investigation Steps

Click on the reset icon icon to reset the diagram.

Be sure to show diagrams, explain why and make specific references to what happened when you constructed triangles.

Was there only one triangle that could be constructed given those parts?
How do you know?

If 5 triangles were constructed with these same "givens", what would have to be true about these triangles?
Are there any lengths that would not work?
(What has to be true about the lengths?)

Certain combinations of sides and/or angles can be used as shortcuts to prove two triangles congruent. These are the conditions in which a triangle is determined.
List the combinations of sides and angles that do work, and explain why.
Then list those that don't work and explain why.