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How do we prove triangles are similar?

Answer: Use any of the 3 theorems : AA, SAS, SSS .

I. AA Theorem

When 2 angles of one triangle are equal to 2 corresponding angles of the other triangle,the two triangles must be similar. Angle Angle theorem similar triangles


III. SSS Theorem

If three pairs of corresponding sides are proportional, then the triangles must be similar. Side Angle Side Picture


II. SAS Theorem

If two sides and the included angle of one triangle are in the same ratio as the corresponding two sides and included angle in another triangle, then the triangles must be similar. Side Angle Side Picture
Practice Problems


Problem 1) Can you use one of the theorems on this page to prove that the triangles are similar?
Answer


Problem 2) Two different versions of triangles HYZ and HIJ. (Assume scale is not consistent). Use the side side side theorem to determine which pair is similar.
Answer


Problem 3) Can you use one of the theorems on this page to prove that the triangles are similar?
Answer

Side Angle Side

Problem 4) Can you use one of the theorems on this page to prove that the triangles are similar?
Answer

Side Angle Side SAS theorem problem

Problem 4) Can you use one of the theorems on this page to prove that the triangles are similar?
Answer

Side Angle Side SAS theorem problem