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Paper, pencil and protractor

The Paper, pencil and protractor: Student worksheet is most effective when students work in groups of three or four. Each student produces their own constructions and the group then compares results.

Three given sides

Some groups will need to cut out the triangles and place them on top of each other to see that they really are transformations of the same triangle. The combination of reflection and rotation is difficult for students to visualise without concrete materials.

Two given sides and an angle

Students will often place the angle in the included position and be unable to draw other configurations. Careful questioning and discussion will help them find the other two possible versions.

Two given angles and one side

If students cannot find alternatives, hint that the angle sum of a triangle will help.

Right-angled triangles with two given side lengths

It is valuable to discuss why there are only two options, one of which is actually the SAS situation. 


It is better for students to do this pen-and-paper activity before they explore the virtual congruence activity.

You can download the Paper, pencil and protractor: Solutions which provide accurate diagrams of all the triangles that can be constructed under the given conditions.