Download 1/07/16 - Topic 9 - Day 2

Name ____________________________ Date ______________ Period ____
Go to: http://illuminations.nctm.org/Activity.aspx?id=3504
You are going to investigate congruence by manipulating the parts (sides and angles) of a
triangle. If you can create two different triangles with the same parts, then those
parts do not prove congruence. So, at the end of the activity, you should be able to
answer the following: Can you prove all the theorems?
Each triangle congruence theorem uses three elements (sides and angles) to prove
congruence.

Select three triangle elements from the top, left menu to start.
(Note: The tool does not allow you to select more than three elements.

If you select the wrong element, simply unselect it before choosing another
element.) This creates those elements in the work area.
ANGLE – SIDE – ANGLE
Click “RESET”

Click Side (AB) –and Angles (A and B).

Move the side AND angles around so that you have made at triangle.

Each point must line up on top of the same letter. So, match “A” to “A”

Once you lined up all the points, move the triangles on top of each other to see if
they are congruent.
Sketch the three triangles that you created.
Is it possible to create another triangle that is not congruent to triangle ABC?
Why? Why not? BE VERY DETAILED
ANGLE – ANGLE – SIDE
Click “RESET”

Click Sides (BC) –and Angles (A and B).

Move the sides and angles around so that you have made at triangle.

Each point must line up on top of the same letter. So, match “A” to “A”

Once you lined up all the points, move the triangles on top of each other to see if
they are congruent.
Sketch the three triangles that you created.
Is it possible to create another triangle that is not congruent to triangle ABC?
Why? Why not? BE VERY DETAILED
ANGLE – ANGLE – ANGLE
Click “RESET”

Click Angles (A, B, and C).

Move the angles around so that you have made at triangle.

Once you lined up all the rays, move the triangles on top of each other to see if
they are congruent.
Sketch the two or three triangles that you created.
Is it possible to create another triangle that is not congruent to triangle ABC?
Why? Why not? BE VERY DETAILED
SIDE – SIDE – ANGLE
Click “RESET”

Click Sides (BC and AC) and Angle (A).

Move the sides and angle around so that you have made at triangle.

Each point must line up on top of the same letter. So, match “A” to “A”

Once you lined up all the points, move the triangles on top of each other to see if
they are congruent.
Sketch the three triangles that you created. In this investigation, it is possible
to create a third triangle that is not congruent given the same
Side-Side-Angle measurements.
Is it possible to create another triangle that is not congruent to triangle ABC?
Why? Why not? BE VERY DETAILED