Similar Triangles: SAS, AA, SSS

Angle Angle Practice problem

Can you use the AA theorem to prove that the two triangles below are similar.

Answer

Yes, the two triangles are similar by AA.

Side Side Side Practice Problems

Below are 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  
Pair #1 are similar triangles because the similarity ratio is always ½ (remember that YI is only half the side of the larger triangle from pair 1).
The problem with pair two involves sides HZ and ZJ. The ratio of these is not consistent with the ratio of the other two pairs of corresponding sides of pair two's triangles. (Again remember that ZJ is not the full segment so to get HJ you must add HZ and ZJ which is 8 and the ratio of 6/8 is not consistent with the ratios of the other sides of pair two)

Side Angle Side Practice Problems

Are the triangles pictured below similar? Use SAS to determine the answer.
  Answer  
Yes, since two pairs of corresponding sides have a 1/3 ratio and the included angle is equal, these two triangles are similar by the Side Angle Side theorem.

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Can you use the Side Angle Side theorem (SAS) to prove that the triangles pictured below similar?
  Answer  
No, although the included angle is equal, the sides do not have a constant ratio 5/15 ≠ 7/20

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Can you use the Side Angle Side theorem (SAS) to prove that the triangles pictured below similar?
  Answer  
No, although we have 2 pairs of sides with an equal ratio of 1/3, we do not have the included angle so we can not state that the triangles are similar.