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IM Geo.3.9 Lesson: Conditions for Triangle Similarity

How could you justify each statement?

 Triangle  is congruent to triangle 

Triangle  is similar to triangle 

Triangle  is congruent to triangle 

Triangle  is similar to triangle 

For each problem, draw 2 triangles that have the listed properties. Try to make them as different as possible: One angle is 45 degrees.

Draw 2 triangles that have the listed properties. Try to make them as different as possible: One angle is 45 degrees and another angle is 30 degrees.

Draw 2 triangles that have the listed properties. Try to make them as different as possible: One angle is 45 degrees and another angle is 30 degrees. The lengths of a pair of corresponding sides are 2 cm and 6 cm.

Compare your triangles with your neighbors’ triangles. Which ones seem to be similar no matter what?

Prove your conjecture.

Here are 2 triangles. One triangle has a 60 degree angle and a 40 degree angle. The other triangle has a 40 degree angle and an 80 degree angle. Explain how you know the triangles are similar.

How long are the sides labeled  and ?

Under what conditions is there an Angle-Angle Quadrilateral Similarity Theorem? What about an Angle-Angle-Angle Quadrilateral Similarity Theorem? Explain or show your reasoning.