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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.