SSS and SAS Similarity Worksheet with Answer Key

What's on the worksheet

1. Decide from side lengths whether two triangles are similar and give the scale factor.
   10, 4, 8 and 6, 15, 129, 12, 7 and 21, 27, 35\sqrt{2}, \sqrt{3}, 2 and 2, \sqrt{6}, 2\sqrt{2}3, 5, 9 and 6, 10, 181.2, 2, 1.6 and 5, 4, 3
2. Decide whether SAS similarity shows each triangle is similar to triangle ABC.
   \triangle PQR with PQ = 10, PR = 15, m\angle P = 48^\circ\triangle KLM with LK = 12, LM = 18, m\angle L = 48^\circ\triangle XYZ with XY = 4, XZ = 6, m\angle Y = 48^\circ\triangle DEF with DE = 18, DF = 12, m\angle D = 48^\circ
3. Find every possible pair of other board lengths for Hannah's garden bed frame.
4. Find every value of x that makes two triangles with given sides similar.
5. Check Sofia's SAS similarity argument for triangles JKL and RST.
6. Find every x for which SAS similarity applies, and write each similarity statement.
7. Prove the midpoint triangle is similar to the original with scale factor one half.