Lesson 4: 7-4: Similar Triangles - SSS and SAS Similarity

1. How do we use SSS and SAS similarity to set up and solve problems involving similar triangles.
2. What are the only criterion we have to prove two triangles are similar?

G.SRT.2
Given two figures, use the definition of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.4
Prove theorems about similarity
G.SRT.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

You can use the SSS or the SAS similarity criteria to prove that two triangles are similar. For SSS, if all three pairs of corresponding side lengths are proportional, then the triangles are similar. For SAS, if the lengths of two sides of one triangle are proportional to the corresponding sides of another triangle, and their included angles are congruent, then the triangles are similar.

The sports store where Miguel works sells 2-person tents and larger 6-person tents with ends shaped like isosceles triangles. Miguel sets up a display with a 2-person tent so that the angle formed at the top of the tent between the two equal length sides is 65 degrees. If he sets up a 6-person tent so that the angle formed at the top of the tent is between the two equal length sides is 65 degrees, are the triangles in the tents similar?

Be sure the congruent angle is between the corresponding proportional sides of each triangle.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections

Formative Assessment

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