Triangle Congruence Activity

Ruler, Protractor, Compass (optional)

Work in pairs. In Steps 1–6, alternate roles so that each of you has a chance to draw the initial triangle.
1 . Draw a triangle on your sheet. Measure two sides and their included angle.
Then tell your partner just those three measurements, and have him or her draw a triangle with those characteristics. Compare your triangles to see whether or not they are congruent.

2. Repeat the process with a new triangle, but this time tell your partner the measures of two sides and a not included angle. Compare your triangles for congruence.
3. Repeat the process with a new triangle, but this time tell your partner the measures of two angles and their included side. Compare your triangles for congruence.
4 . This time, tell your partner the measures of all three angles of your triangle. Compare your triangles for congruence.

5. Now, tell your partner the measures of two angles and a side opposite one of the angles.
Compare your triangles for congruence.

6. Tell your partner the measure of all three sides of your triangle. (Hint: Making this triangle might be a bit tougher; use the figure at the right as a hint.) Compare your triangles for congruence.
7 . List any conditions you discovered that seem to guarantee congruent triangles -> Which of these could you prove based on other conditions? (So which must be postulates, and which could be theorems)