Check for Understanding – p. 256 #1-11  ABC ~  DEF. True or False? 1.  BAC ~  EFD 2. If m  D = 45 , then m  A = 45  3. If m  B = 70 , then m  F = 70  4. C A B F E D False True False

Check for Understanding – p. 256 #1-11  ABC ~  DEF. True or False? If DF:AC = 8:5, then m  D:m  A = 8:5 7. If DF:AC = 8:5, then EF:BC = 8:5 8. If the scale factor of  ABC to  DEF is 5 to 8, then the scale factor of  DEF to  ABC is 8 to 5. C A B F E D True False True

We could prove that two triangles are similar by verifying that the triangles satisfy the two pieces of the definition of similar polygons 1. the corresponding angles are congruent, and 2. The corresponding sides follow the same scale factor throughout the figure. However, when dealing with triangles, specifically, there are simpler methods.

Postulate 15 – AA Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. Ex. If  A   D and  B   E, then  ABC ~  DEF AC B D F E

Check for Understanding – p. 256 # One right triangle has an angle with measure 37 . Another right triangle has an angle with measure 53 . Are the two triangles similar? Explain. Yes, AA Similarity Postulate. 37° 53° 37°

Theorem 7-1 SAS Similarity Theorem If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar. A B C DF E If:  A   D Then:  ABC ~  DEF

Theorem 7-2 SSS Similarity Theorem If the sides of two triangles are in proportion, then the triangles are similar. B C D E A F If: Then:  ABC ~  DEF

Check for Understanding p #1-6 Can the two triangles shown be proved similar? If so, state the similarity and tell which postulate or theorem is used R S X F H G  HFG ~  RXS E C D N UJ 70  40  60  70  Not Similar SSS Similarity Thm.

Check for Understanding p #1-6 Can the two triangles shown be proved similar? If so, state the similarity and tell which postulate or theorem is used R Q S U T  RQS ~  UTS V W X Z Y No Conclusion SAS Similarity Theorem

Check for Understanding p #1-6 Can the two triangles shown be proved similar? If so, state the similarity and tell which postulate or theorem is used. 5. L  LNP ~  ANL 25 A P N9 15 P N L N L A 25 9 SAS Similarity Thm.

6. B A C D Check for Understanding p #1-6 Can the two triangles shown be proved similar? If so, state the similarity and tell which postulate or theorem is used. BC A A C D These Triangles are NOT Similar!

Problem Solving Linda wants to determine the height of this tree. She measured the shadow of the tree as 8m and her own shadow was 3m. She knows that she is 1.5m tall. How tall is the tree? 8m 3m 1.5m x 3x = 12; x = 4 4m