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8.4 Similar Triangles

8.4 Similar Triangles. Number Talk. The scale on a map is 6cm : 2kn. If the distance between two cities is 8kn, how far apart in cm are the two cities on the map?. In Chemistry Class there is a girl to boy ratio of 5 : 8. If there are a total of 39 students, how many boys are there?.

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8.4 Similar Triangles

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  1. 8.4 Similar Triangles

  2. Number Talk The scale on a map is 6cm : 2kn. If the distance between two cities is 8kn, how far apart in cm are the two cities on the map? • In Chemistry Class there is a girl to boy ratio of 5 : 8. If there are a total of 39 students, how many boys are there? In Geometry Class, the girl to boy ratio is 8 to 6. If there are a total of 42 students, how many girls are there?

  3. How did we do?

  4. Let’s Try

  5. Similar Triangles • Given the triangles are similar. Find the value of the variable. Left side of sm Δ Base of sm Δ Left side of lg Δ Base of lg Δ = 6 5 > 2 6h = 40 > h

  6. ∆ABC is similar to ∆DBE. A 5 D y 9 x B C E 8 4

  7. Agenda • Number talk expectations • Number talk • Warm up • Discuss the Angle Angle Theorem

  8. Number Talk • Name the rule!

  9. Warm Up • Given the triangles are similar. Find the value of the variable. )) m )) ) 10 42 ) 20

  10. Postulate 25 • Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

  11. Determine whether the triangles are similar. 6 32° 33° 9 18 No, because two angles of one triangle are not congruent to two angles of another triangle.

  12. Determine whether the triangles are similar. 60° 60° 60° 60° Yes, because two angles of one triangle are congruent to two angles of another triangle.

  13. Decide whether two triangles are similar, not similar, or cannot be determined. A 92° S 41° 92° 57° S + 92 + 41 = 180 S + 133 = 180 S = 47 A + 92 + 57 = 180 A + 149 = 180 A = 31 31° 47° Not similar

  14. Given two triangles are similar, solve for the variables. 2b - 8 a + 3 14 15 16 ) ) 10 15(a+3) = 10(16) 15a + 45 = 160 15a = 115

  15. 2 Practice Problems • For each problem. Show your solutions mathematically as well as explain what you did in plain English. • For Example • “When setting up the proportion 4/x = 15/5 I knew that EB corresponds with DC and EA corresponds with AD.”

  16. Take Exit Slip on IPAD • Test ID: 0881886769 • Re Take Yesterday’s Formative: 6461882153

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