Congruent Triangles Project . . . . . . . . . . . . . . . . . . . . . Name(s):________________________________________

Refer to the Constructing Triangles Worksheet in answering the questions below. The questions will require explanations and diagrams. Be sure to explain why, in each question, and make specific references to what happened when you constructed triangles on the worksheet. You may answer on this sheet, or on your own paper.

1) You constructed a triangle given the three sides. 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?)

2) You constructed a triangle given two angles and a side. 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 side-lengths or angle-measures that would not work?

3) You constructed a triangle given three angles. 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 angle-measures that would not work?

4) In several problems, you constructed a triangle given two sides and an angle. 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? Discuss all cases.

5) Explain what "determine" means (as used in the phrase "two sides and the included angle determine a triangle").

6) One way to prove two triangles congruent is using the definition of congruent triangles. Is this the way we usually prove triangles congruent? Why or why not?

7) Certain combinations of sides and/or angles can be used as shortcuts to prove two triangles congruent (SAS, etc). 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.