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- 1. #3.19 Geo. Drill 3/5/14 • Given that the following two pentagons are similar, find x. 8 12 4 6 x 14 5 4 10
- 2. #3.19 Geo. Drill 3/5/14 • Given that the following two pentagons are similar, find x. 8 12 4 6 x 14 5 4 10
- 3. Geometry Drill •Can you list the 5 ways to prove triangles congruent
- 4. Objective • Students will use the similarity postulates to decide which triangles are similar and find unknowns.
- 5. Congruence vs. Similarity •Congruence implies that all angles and sides have equal measure whereas...
- 6. Congruence vs. Similarity •Similarity implies that only the angles are of equal measure and the sides are proportional
- 7. AA Similarity Postulate •Two triangles are similar if two pairs of corresponding angles are congruent
- 8. AA Similarity Postulate E B A C D F
- 9. SAS Similarity Postulate •Two triangles are similar if two pairs of corresponding sides are proportional and the included angles are congruent
- 10. SAS Similarity Postulate E B 12 8 A 4 C D 6 F
- 11. SSS Similarity Postulate •Two triangles are similar if all three pairs of corresponding sides are proportional.
- 12. SSS Similarity Postulate E B 9 13 A 7 C 21 27 D 39 F
- 13. Example 1 •∆APE ~ ∆DOG. If the perimeter of ∆APE is 12 and the perimeter of ∆DOG is 15 and OG=6, find the PE.
- 14. Example 2 Explain why ∆ABE ~ ∆ACD, and then find CD. Step 1 Prove triangles are similar. A A by Reflexive Property of , and B C since they are both right angles. Therefore ∆ABE ~ ∆ACD by AA ~.
- 15. Step 2 Find CD. Corr. sides are proportional. Seg. Add. Postulate. x(9) = 5(3 + 9) 9x = 60 60 20 x 9 3 Substitute x for CD, 5 for BE, 3 for CB, and 9 for BA. Cross Products Prop. Simplify. Divide both sides by 9.
- 16. Explain why ∆RSV ~ ∆RTU and then find RT. Step 1 Prove triangles are similar. It is given that S T. R R by Reflexive Property of . Therefore ∆RSV ~ ∆RTU by AA ~.
- 17. Check It Out! Example 3 Continued Step 2 Find RT. Corr. sides are proportional. Substitute RS for 10, 12 for TU, 8 for SV. RT(8) = 10(12) 8RT = 120 RT = 15 Cross Products Prop. Simplify. Divide both sides by 8.
- 18. Writing Proofs with Similar Triangles Given: 3UT = 5RT and 3VT = 5ST Prove: ∆UVT ~ ∆RST
- 19. Example 4 Continued Statements Reasons 1. 3UT = 5RT 1. Given 2. 2. Divide both sides by 3RT. 3. 3VT = 5ST 3. Given. 4. 4. Divide both sides by3ST. 5. RTS VTU 5. Vert. s Thm. 6. ∆UVT ~ ∆RST 6. SAS ~ Steps 2, 4, 5
- 20. Given: M is the midpoint of JK. N is the midpoint of KL, and P is the midpoint of JL. Prove: ∆JKL ~ ∆NPM
- 21. Statements Reasons 1. M is the mdpt. of JK, N is the mdpt. of KL, and P is the mdpt. of JL. 1. Given 2. 2. ∆ Midsegs. Thm 3. 4. ∆JKL ~ ∆NPM 3. Div. Prop. of =. 4. SSS ~
- 22. Example 5: Engineering Application The photo shows a gable roof. AC || FG. ∆ABC ~ ∆FBG. Find BA to the nearest tenth of a foot. From p. 473, BF 4.6 ft. BA = BF + FA 6.3 + 17 23.3 ft Therefore, BA = 23.3 ft.
- 23. Check It Out! Example 5 What if…? If AB = 4x, AC = 5x, and BF = 4, find FG. Corr. sides are proportional. Substitute given quantities. 4x(FG) = 4(5x) FG = 5 Cross Prod. Prop. Simplify.
- 24. Conclusion •Similarity •AA •SAS •SSS
- 25. Classwork/Homework •Page 474-475 #’s 110, 17,18, 23, 24, 44-46

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