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Cut out the large triangle and the three pieces (A, B, and C) along the dotted lines. Make sure to cut as
close to the solid line as possible.
1. Arrange the three solid lines you just cut out so they form a triangle. Compare your triangle to the
triangle you cut out. What do you notice about the triangles?
Look at your partner’s triangles. Do they have the same results?
Is there a way to arrange the solid lines so they don’t create a triangle that’s congruent?
If all three sides of a triangle are congruent to the sides of another triangle, then the triangles are
____________________.
2. Line up the solid lines on the angle below so that piece A lines up with the A on the angle. Finish the
triangle with the third piece.
A
1
C
Compare the triangle you just made with the one you cut out. What do you notice about the two
triangles?
Do the same thing with the angles below. Explain in your own words what is happening.
A
2
C
B
3
B
If two sides and the included angle of one triangle are congruent to two sides and the included angle of
another triangle then the two triangles are __________________.
3. The figure below gives you two angles with one of the sides between them. Finish the triangle.
Arrange your pieces on the triangle. How many ways could you arrange the other two pieces to
complete the triangle?
Compare your triangle with the one you cut out. Explain what you notice about the triangle you drew
and the one you cut out?
Do the same with the angles and side on the right.
Compare this triangle with the one you cut out
and explain what you notice.
If two triangles have congruent angles with a congruent
side in between, then the triangles are _________________.
4. Cut out the two angles with the one side. Arrange them with the other two sides into a triangle.
Look at your partner and see if you have the same triangle. Compare both your triangles with the one
you cut out earlier.
If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding
nonincluded side of another triangle, then the triangles are _________________.
A
2
B
1
C
3