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.