Allie Terrell & Katie Cooper Advanced Geometry 3rd period Ms. Thompson

LEARNING TARGET I can use triangle similarity to solve unknown sides and angles.

VOCABULARY Similar – two shapes are similar if they have the same number of sides, the same number of angles, and the same angle measure.

Similar triangles are triangles that have the same shape but not necessarily the same size. D F E ABC  DEF A  D B  E AB DE BC EF AC DF = = C  F

Six of those statements are true as a result of the similarity of the two triangles. However, if we need to prove that a pair of triangles are similar how many of those statements do we need? Because we are working with triangles and the measure of the angles and sides are dependent on each other, we do not need all six. There are three special combinations that we can use to prove similarity of triangles. 1. SSS Similarity Theorem  3 pairs of proportional sides 2. SAS Similarity Theorem  2 pairs of proportional sides and congruent angles between them 3. AA Similarity Theorem  2 pairs of congruent angles

ABC  DFE E F D 1. SSS Similarity Theorem  3 pairs of proportional sides 9.6 10.4 A B C 5 13 12 4 ABC  DFE

GHI  LKJ mH = mK 2. SAS Similarity Theorem  2 pairs of proportional sides and congruent angles between them L J K 7.5 G H I 5 70 70 7 10.5 mH = mK GHI  LKJ

The SSA Similarity Theorem does not work The SSA Similarity Theorem does not work. The congruent angles should fall between the proportional sides (SAS). For instance, if we have the situation that is shown in the diagram below, we cannot state that the triangles are similar. We do not have the information that we need. L J K 7.5 G H I 5 50 7 50 10.5 Angles I and J do not fall in between sides GH and HI and sides LK and KJ respectively.

MNO  QRP mN = mR mO = mP 3. AA Similarity Theorem  2 pairs of congruent angles Q P R M N O 70 50 50 70 mN = mR MNO  QRP mO = mP

TSU  XZY mT = mX mS = mZ It is possible for two triangles to be similar when they have 2 pairs of angles given but only one of those given pairs are congruent. S T U X Y Z 34 34 34 34 59 59 mT = mX 87 59 mS = mZ mS = 180- (34 + 87) TSU  XZY mS = 180- 121 mS = 59

Sage and Scribe Work with your partner. Only one paper per partner. Page 483 #10-26 and 40-46 (EVEN # ONLY) Page 492 #2- 14 (EVEN # ONLY)

REFERENCES www.dictionary.com paccadult.lbpsb.qc.ca/eng/extra/img/Similar%20Triangles.ppt www.mente.elac.org/presentations/sim_tri_I.pps