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Similar Triangles 8.3

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**Identify similar triangles.**

Learn the definition of AA, SAS, SSS similarity. Use similar triangles to solve problems. homework

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**BCA ECD by the Vertical Angles Theorem. **

Explain why the triangles are similar and write a similarity statement. BCA ECD by the Vertical Angles Theorem. Also, A D by the Right Angle Congruence Theorem. Therefore ∆ABC ~ ∆DEC by AA Similarity. homework

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**D H by the Definition of Congruent Angles.**

Explain why the triangles are similar and write a similarity statement. D H by the Definition of Congruent Angles. Arrange the sides by length so they correspond. Therefore ∆DEF ~ ∆HJK by SAS Similarity. homework

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**Arrange the sides by length so they correspond.**

Explain why the triangles are similar and write a similarity statement. Arrange the sides by length so they correspond. Therefore ∆PQR ~ ∆STU by SSS similarity. homework

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**TXU VXW by the Vertical Angles Theorem.**

Explain why the triangles are similar and write a similarity statement. TXU VXW by the Vertical Angles Theorem. Arrange the sides by length so they correspond. Therefore ∆TXU ~ ∆VXW by SAS similarity. homework

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**Explain why the triangles are similar and write a **

similarity statement. By the Triangle Sum Theorem, mC = 47°, so C F. B E by the Right Angle Congruence Theorem. Therefore, ∆ABC ~ ∆DEF by AA Similarity. homework

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**Therefore, ∆ABC ~ ∆DEF by AA Similarity.**

Determine if the triangles are similar, if so write a similarity statement. By the Definition of Isosceles, A C and P R. By the Triangle Sum Theorem, mB = 40°, mC = 70°, mP = 70°, and mR = 70°. Therefore, ∆ABC ~ ∆DEF by AA Similarity. homework

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**Explain why ∆ABE ~ ∆ACD, and then find CD.**

Prove triangles are similar. A A by Reflexive Property, and B C since they are right angles. Therefore ∆ABE ~ ∆ACD by AA similarity. x(9) = 5(12) 9x = 60 homework

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**Explain why ∆RSV ~ ∆RTU and then find RT.**

Prove triangles are similar. It is given that S T. R R by Reflexive Property. Therefore ∆RSV ~ ∆RTU by AA similarity. RT(8) = 10(12) 8RT = 120 RT = 15 homework

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**Given RS || UT, RS = 4, RQ = x + 3, QT = 2x + 10, UT = 10, find RQ and QT.**

Since because they are alternate interior angles. By AA Similarity, ΔRSQ ~ ΔTUQ. Using the definition of similar polygons, RQ = 8; QT = 20

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**Determine if the triangles are similar, if so write a similarity statement.**

35 45 100 Find the missing angles. Check for proportional sides. AA Similar AEZ ~ REB SAS Similar AGU ~ BEF Check for proportional sides. Check for proportional sides. SSS Similar ABC ~ FED homework Not Similar

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**Determine if the triangles are similar, if so write a similarity statement.**

Alternate Interior angles. Vertical angles. Check for proportional sides. Sides do not correspond. Not Similar. AA Similar FGH ~ KJH Not Similar. Find the missing angles. 120 45 Check for proportional sides. Check for proportional sides. Not Similar. Not Similar. Not Similar. homework

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**Given ABC~EDC, AB = 38.5, DE = 11, AC = 3x + 8, and CE = x + 2, find AC and CE.**

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**Each pair of triangles below are similar, find x.**

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Assignment Section 11 – 36

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