Name_______________________________________
Similar Triangles Project
Due ______________
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You will create a picture of a noun with at least 18 triangles (similar triangles) on an 11in X
14in poster board or construction paper. Make sure you include a title of your noun on the top
of your poster board.
You will be making 6 triangles using AA similarity, 6 triangles using SSS similarity and 6
triangles using SAS similarity
You may NOT use the same scale factor for any of the similar triangles that you create.
Use the handouts to create your similar triangles. You will have to turn in the handouts, so
PHOTOCOPY onto white or colored paper your triangles to design your noun poster. If you
use white paper, color your triangles using markers or colored pencils.
If you want to use more than 18 triangles you may reuse any of the triangles you have created
but you may not make new triangles.
Write a paragraph that:
o Defines each of the triangle similarities (AA, SSS, SAS).
o Describes the difference between triangle similarity and triangle congruence
o Describe what happens to your new triangles when you multiply your original triangle by
a scale factor less than one and greater than one.
o Explain why your calculations of proportions and the sum of angle measurements might
not be exact.
o Explain any difficulties that your many have had with this project and if this project
helped you understand triangle similarity.
Name_______________________________________
Rubric
Points
Picture is a noun with at least 18 triangles
_____ / _____
Triangles are neatly colored, cut and glued to an
11x14 poster board
_____ / _____
Triangles are neatly drawn on the paper provided.
The measurements of the lengths of the sides are
given in centimeters and the angle measurements are
given.
_____ / _____
Calculations are accurate
_____ / _____
Similarity statement, scale factor and sum
of angles are provided.
_____ / _____
Paragraph written.
_____ / _____
TOTAL:
_____ / _____
Name_______________________________________
AA Similarity
Step 1: Create a line segment. Label the endpoints A and B. Measure in centimeters (cm).
Step 2: From point A, use your protractor to measure an acute angle (you choose the angle measurement) and
make a point. Label the angle with the measurement. Draw a line from point A through the new point.
Step 3: Repeat Step 2 from point B.
Step 4: Where the 2 new lines intersect is point C. You should now have a triangle.
Step 5: Measure the sides of the triangle in cm.
Step 6: Create a second triangle that is similar to the first one that you created. Start with a line segment that is
different than the original and repeat steps 2-5. Call this triangle A’B’C’.
Step 7: Create a third triangle that is similar to the first one that you created. Start with a line segment that is
different than the first 2 triangles and repeat steps 2-5 again. Call this triangle A”B”C”.
Step 8: Start all over from step 1 to create a second set of 3 triangles but call these triangles XYZ, X’Y’Z’ and
X”Y”Z”.
Step 9: Provide a similarity statement.
Step 10: Show that the triangles are similar by providing a ratio of corresponding sides of the original triangle to
the new triangle. Change your fraction into a decimal. This is the scale factor. You should have 3 fractions that
are equal to each other (or very close!)
Step 11: Add all 3 angle measurements. Don’t just give your answer; make sure you show the angle measures.
Triangles ABC, A’B’C’ and A”B”C”
Similarity statements ________________________
_____________________________
Scale Factors
_____________________________
_________________________
Sum of triangle angles ____+____+____=____, ____+____+____=____, ____+____+____=____
Name_______________________________________
AA Similarity
Triangles XYZ, X’Y’Z’ and X”Y”Z”
Similarity statements ________________________
_____________________________
Scale Factors
_____________________________
_________________________
Sum of triangle angles ____+____+____=____, ____+____+____=____, ____+____+____=____
Name_______________________________________
SSS Similarity
Step 1: Create a triangle. Measure and label the sides in cm. Label the vertices of the triangle CAT
Step 2: Choose a scale factor that is less than 1.
Step 3: multiply each side of the triangle by the scale factor.
Step 4: Create a new triangle with your new side measurements. Call your new triangle C’A’T’. (hint- it might help
to measure one angle from your original triangle. Use the same angle measurement on the corresponding angle
of your new triangle to help draw your new triangle.
Step 5: repeat steps 2-4 but this time use a scale factor that is greater than 1. Name your triangle C”A”T”.
Step 6: Repeat steps 1-5 for your second set of triangles using SSS similarity. Side lengths must be different.
Name your triangles DOG, D’O’G’ and D”O”G”.
Step 7: Provide a similarity statement.
Step 8: Show that the triangles are similar by providing a ratio of corresponding sides of the original triangle to the
new triangle. Change your fraction into a decimal. This is the scale factor. You should have 3 fractions that are
equal to each other (or very close!)
Step 9: Provide the sum of the angle measures.
Triangles CAT, C’A’T’, C”A”T”
Similarity statements ________________________
_____________________________
Scale Factors
_____________________________
_________________________
Sum of triangle angles ____+____+____=____, ____+____+____=____, ____+____+____=____
Name_______________________________________
SSS Similarity
Triangles DOG, D’O’G’, D”O”G”
Similarity statements ________________________
_____________________________
Scale Factors
_____________________________
_________________________
Sum of triangle angles ____+____+____=____, ____+____+____=____, ____+____+____=____
Name_______________________________________
SAS Similarity
Step 1: Create a line segment. Label the endpoints P and G. Measure in centimeters (cm).
Step 2: From point P, use your protractor to measure an acute angle (you choose the angle measurement) and
make a point and name the point I. Label the angle with the measurement. Draw a line from point P to point I.
Measure the line segment PI in cm.
Step 3: Create a triangle by connecting point I and point G. Measure the line segment IG in cm.
Step 4: Choose a scale factor that is less than 1.
Step 5: Multiply segments PG and PI by the scale factor, this with be the lengths of segments P’G’ and P’I’. Draw
segment P’G’ first. From point P’ and using the same angle measurement that you chose from step 2 to create
segment P’I’.
Step 6: Create your new triangle P’I’G’ by connecting points I’ and G’. Measure segments I’G’.
Step 7: repeat steps 2-6 but this time use a scale factor that is greater than 1. Name your triangle P”I”G”.
Step 8: Start all over from step 1 to create a second set of 3 triangles but call these triangles RAT, R’A’T’ and
R”A”T”.
Step 9: Provide a similarity statement.
Step 10: Show that the triangles are similar by providing a ratio of corresponding sides of the original triangle to
the new triangle. Change your fraction into a decimal. This is the scale factor. You should have 3 fractions that
are equal to each other (or very close!).
Step 11: Add all 3 angle measurements. Don’t just give your answer; make sure you show the angle measures.
Triangles PIG, P’I’G’, P”I”G”
Similarity statements ________________________
_____________________________
Scale Factors
_____________________________
_________________________
Sum of triangle angles ____+____+____=____, ____+____+____=____, ____+____+____=____
Name_______________________________________
Triangles RAT, R’A’T’, R”A”T”
Similarity statements ________________________
_____________________________
Scale Factors
_____________________________
_________________________
Sum of triangle angles ____+____+____=____, ____+____+____=____, ____+____+____=____