Download Warm-Ups

Proving Side-Side-Side
• Create a triangle with the follow side lengths:
4 inches, 6 inches, and 8 inches.
• Create a second triangle using a scale factor of
2.5.
• Create a third triangle using a scale factor
4
of .
5
• Determine if these three triangles are similar
by measuring the angles.
Proving Side-Angle-Side
• Create a 55° angle. Its two sides should be 3.5 and
5 inches long. Enclose your angle to make a
triangle.
• Create a second 55° angle. Use a scale factor of ¾
to find the length of your sides. After creating
these sides, enclose your angle to make a
triangle.
• Create a third 55° angle. Use a scale factor of 2 to
find the length of your sides. After creating these
sides enclose your angle to make a triangle.
Determine if your three triangles are similar by
finding the measure of the third side and other two
angles.
Side-Side-Side Similarity Theorem
(SSS)
• If the corresponding side lengths of two
triangles are proportional then the triangles
are similar.
Using Side-Side-Side
SAS Similarity Theorem
• If an angle of one triangle is congruent to an
angle of a second triangle and the lengths of
the sides including these angles are
proportional then the triangles are similar.
Using SAS- Try this on your own!
Angles and Similar Triangles
Question: What can you conclude about two triangles if you know two
pairs of corresponding angles are congruent?
– Step 1: Draw △EFG so that m∠E=40° and the m∠G=50°.
– Step 2: Draw △RST so that m∠R=40° and the m∠G=50°. And △RST
is not congruent to △EFG.
– Step 3: Calculate m∠F and m∠S using the Triangle sum Theorem.
Use a protractor to check that your results are true.
– Step 4: Measure and record the side lengths of both triangles. Use
centimeters.
Draw Conclusions:
• Are the triangles similar? Explain your reasoning.
• Repeat the steps above using different angle measures. Make a
conjecture about two triangles with two pairs of congruent
corresponding angles.
• Define the Angle-Angle Similarity Postulate in your own words
Angle-Angle (AA) Similarity Postulate
• If two angles of one triangle are congruent to
two triangles of another triangle, then the two
triangles are similar.
Example
• Determine whether the triangles are similar. If
they are, write a similarity statement. Explain
your reasoning.
Example
Show that the two triangles are similar.