Proofs by Construction


Sue Meredith

Seventh graders are not ready for formal two-column proofs, however, they can be exposed to them. They are ready to follow a systematic process to construct congruent triangles by copying the three sides, SSS; coping two sides with the included angle, SAS; and copying two angles with the included side, ASA.


Copying a triangle with SSS:

(Click here to see the step by step process of copying the three sides.)

Copying a triangle with SAS:


(Click here to see step-by-step process of constructing a congruent triangle by side, included angle, and side.)


Copying a triangle with ASA.

(Click here to see the step by step procedure to copy a triangle with angle, included side, and angle.)


Another construction activity can be used to prove the properties of squares. Have students construct squares so that they retain the characteristics of a square. In so doing, the students must apply the properties of squares.

Click here for further explanation of some possible constructions.