Exploring Similar Triangles
Name:________________________
Hour:___________
What you will need: Paper, Pen/Pencil, Tracing paper, Ruler, Straight edge
You and your group will be exploring Angle-Angle Similarity (AA~). Work together through the
following steps and answer each question. Record your answers individually.
Step 1: On a separate piece of paper, draw a triangle of any size using a straight edge.
Step 2: Use a ruler to CAREFULLY measure and label the length of each side.
Side 1:
Side 2:
Side 3:
Step 3: Using a piece of tracing paper, trace two angles of your original triangle, make sure the distance
between the two angles is different than your original triangle. Using these traced angles, construct a
new triangle that has all different side lengths than the original triangle, but that shares two angles with
the original triangle. Use a straight edge.
Hint: Use the tracing paper to compare angles to be sure they are congruent to the original
triangle.
Step 4: How do all three angles of each triangle compare? Use the tracing paper to check!
Step 5: With a ruler, carefully measure and label the sides of your new triangle.
New triangle
Side 1:
Side 2:
Side 3:
Original Triangle
Ratio of new to old
Exploring Similar Triangles
Name:________________________
Hour:___________
Step 6: Answer the following:
1. What is the ratio of the lengths of corresponding sides?
2. Are the triangles similar? Explain why or why not.
3. Is this true of all your group members’ triangles? What were their similarity ratios?
4. Finish this conjecture….
If two angles of one triangle are congruent to two of another triangle, then the triangles are
_________________.
We call this Angle-Angle Similarity and write AA~
Exploring Similar Triangles
Name:________________________
Hour:___________
What you will need: Paper, Pen/Pencil, Tracing paper, Ruler, Straight edge
You and your group will be exploring Side-Angle-Side Similarity (SAS~). Work together through
the following steps and answer each question. Record your answers individually.
Step 1: On a separate piece of paper, draw a triangle of any size with a straight edge.
Step 2: Use a ruler to CAREFULLY measure and label the length of each side.
Side 1:
Side 2:
Side 3:
Step 3: Choose two of your sides. Scale the two sides by any number (don’t get too big). Each member in
your group should have a different scale.
Scale factor you used:________
Step 4: Mark the angle where your two sides meet. Using tracing paper, trace this angle. Draw your new
scaled sides off this angle. For example:
Step 5: Connect your two lines to form a new triangle.
Exploring Similar Triangles
Name:________________________
Hour:___________
Step 6: Given that two corresponding sides are proportional and one angle is congruent (Side-AngleSide), check if your two triangles are similar:
1. Are the triangles similar? Explain why or why not.
2. Is this true of all your group members’ triangles? What were their similarity ratios?
3. Given your Side, Angle, and Side, could you or your group members have created a triangle
that was not similar to the original triangle? Explain your reasoning.
4. Finish this conjecture….
If an angle of one triangle is congruent to an angle of a second triangle, and the sides
including the two angles are proportional, then the triangles are ______________.
We call this Side-Angle-Side Similarity and write SAS~
Exploring Similar Triangles
Name:________________________
Hour:___________
What you will need: Paper, Pen/Pencil, Tracing paper, Ruler, Straight edge, straws
You and your group will be exploring Side-Side-Side Similarity (SSS~). Work together through the
following steps and answer each question. Record your answers individually.
Step 1: On a separate piece of paper, use a ruler and straight edge to draw and label a triangle with sides
of length 6-8-10. Draw a second triangle on your tracing paper that has sides of length 9-12-15.
Step 2: Answer the following:
1. What is the ratio of the lengths of corresponding sides? Hint: Make a table to organize your
sides.
2. Are corresponding angles congruent?
Hint: Use the tracing paper to compare angle measurements.
3. Are the two triangles similar? Explain.
Step 3: Use the straws you were given to create two triangles. With a ruler, measure the sides of your
triangles, draw and label your triangles below:
Exploring Similar Triangles
Name:________________________
Hour:___________
Step 4: Answer the following:
1. Are the corresponding sides of your triangles proportional? If yes, what is the similarity ratio?
Triangle 1
Triangle 2
Side 1:
Side 2:
Side 3:
2. What do you notice about the angles?
Can you manipulate the sides so that sides are still proportional, but corresponding angles are
not congruent? Explain. Did your group members have similar findings?
3. Finish this conjecture….
If the corresponding sides of two triangles are proportional, then the triangles are
_________________.
We call this Side-Side-Side Similarity and write SSS~