This is sufficient information by the SSS Similarity Theorem to determine that the triangles are similar. 2 _ RT ST RS _ _ _ 3 XZ YZ XY Example 3Ĭhoice B If =, then you know that all the sides are proportional by the same scale factor.

Therefore, this is not sufficient information. You do not, however, know whether that scale factor is as determined by. 2 2 _ _ RS _ 3 3 XY Example 3Ĭhoice A If =, then you know that the other two sides are proportional. Check each answer choice until you find one that supplies sufficient information to prove that ΔRST ~ ΔXYZ. Solve the Test Item Since =, you know that these two sides are proportional at the scale factor of. Read the Test Item You are given that = and asked to identify which additional information would be sufficient to prove that ΔRST ~ ΔXYZ. If ΔRST and ΔXYZ are two triangles such that = which of the following would be sufficient to prove that the triangles are similar?AěC R  Sĝ 2 _ RS _ 3 XY Example 3 A.ΔAFE ~ ΔABC by SSS Similarity Theorem B.ΔAFE ~ ΔACB by SSS Similarity Theorem C.ΔAFE ~ ΔAFC by SSS Similarity Theorem D.ΔAFE ~ ΔBCA by SSS Similarity Theorem Example 2 If so, choose the correct similarity statement to match the given data.

Determine whether the triangles are similar. A.ΔPQR ~ ΔSTR by SSS Similarity Theorem B.ΔPQR ~ ΔSTR by SAS Similarity Theorem C.ΔPQR ~ ΔSTR by AAA Similarity Theorem D. Answer:Since the lengths of the sides that include M are proportional, ΔMNP ~ ΔMRS by the SAS Similarity Theorem. Use the SSS and SAS Similarity Theorems B.Determine whether the triangles are similar. Answer:So, ΔABC ~ ΔDEC by the SSS Similarity Theorem. Use the SSS and SAS Similarity Theorems A.Determine whether the triangles are similar. Use the AA Similarity Postulate Answer:So, ΔQXP ~ ΔNXM by the AA Similarity. QXP NXM by the Vertical Angles Theorem. Answer:So, ΔABC ~ ΔDEC by the AA Similarity. Use the AA Similarity Postulate By the Triangle Sum Theorem, 42 + 58 + mA = 180, so mA = 80. Since mB = mD, B D Since mE = 80, A E.

Aa similarity postulate