Proving Side-Side-Side. 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.

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Presentation transcript:

Proving Side-Side-Side

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.