Download CONGRUENT TRIANGLES

CONGRUENT TRIANGLES
Yesterday, we discovered that congruent polygons meant that all angles and all sides are
congruent. Mathematicians are lazy, so we are always looking for shortcuts. Do I need
to measure all six parts (three sides and three angles) of every triangle to figure out what
triangles are congruent? If not, what is the minimum amount of parts I need?
Object: To determine the minimum amount necessary to prove two triangles are
congruent and determine if it matters what parts I have.
Materials:
An envelope with different K’nex parts
Rules: The orange angle is the same as the middle yellow angle. If the instructions say
to use the yellow angle it means the biggest yellow angle (90).
Steps:
1. How many different triangles can you make using one red side? Record the
number you made here. Could we prove two triangles congruent knowing only
one side?
2. How many different triangles can you make using one orange angle? Record that
number here. Could we prove two triangles congruent knowing only one angle?
3. How many different triangles can you make using one orange angle and one red
piece? Could we prove two triangles congruent having one side and one angle?
How many different triangles can you make using two orange angles? Could you
prove two triangles congruent knowing two angles?
4. How many different triangles can you make using two black sides and one yellow
side? Could you prove two triangles congruent knowing three sides?
5. How many different triangles can you make using two orange angles and one
yellow angle? Could you prove two triangles congruent knowing three angles?
6. How many different triangles can you make if you have one gray side, one yellow
side and one orange angle and the orange angle has to be between the gray and
yellow side? Could you prove two triangles congruent knowing two sides and the
angle between them?
7. Take one yellow side and attach it to one orange angle. Now take a black side,
but don’t attach to the orange angle that you already have. How many different
triangles can you make using a yellow side attached to the orange angle and then
a black side not attached to that orange angle? Could you prove two triangles
congruent knowing two sides and an angle not between them?
8. How many different triangles could you make using one orange angle, one yellow
angle and one gray side if the gray side is attached to both of those angles? Could
you prove two triangles congruent knowing two angles and the side between
them?
9. How many different triangles could you make using one orange angle, one yellow
angle and one red side that is only attached to the orange angle? Could you prove
two triangles congruent knowing two angles and the side not between them?
10. How many different triangles can you make using a purple side and a red side
attached to the yellow angle? Could you prove two triangles congruent, knowing
you have a right triangle and two sides of the right triangle?
11. Which problems resulted in having congruent triangles? Which ones didn’t?