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Solve for x:

Solve for x:. x+3 = _ 5_ 2x 7. Proportions and Similar Triangles. Geometry Unit 11, Day 8 Ms. Reed. Proportions and Similar Triangles. We will be investigating ways proportional relationships in triangles You will need: Paper Ruler Protractor Calculator. On your paper:.

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Solve for x:

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  1. Solve for x: x+3 = _5_ 2x 7

  2. Proportions and Similar Triangles Geometry Unit 11, Day 8 Ms. Reed

  3. Proportions and Similar Triangles • We will be investigating ways proportional relationships in triangles • You will need: • Paper • Ruler • Protractor • Calculator

  4. On your paper: • Construct a triangle, label it ABC • Create a line parallel to AC. Call the intersection point on AB, D and the point on BC, E. • Measure DB, DA, BE, and EC • Compare the ratios of BD/DA and BE/EC • WHAT DO YOU NOTICE?

  5. Conclusion • If a line is parallel to one side of the triangle and intersects the other two sides, then it divides those sides proportionally. • This is called the Side-Splitter Theorem

  6. Example 1 • Set up the proportion • x =8 x 5 16 10

  7. Example 2 • Solve for x • x = 1.5 5 3 2.5 x

  8. On your paper: • Create 3 Parallel Line • Draw 2 transversals through the lines so it looks like this: • Label as shown a c b d

  9. What do you notice? • Measure a, b, c and d. • Compare the relationship between a/b and c/d. • WHAT DO YOU NOTICE?

  10. What we discovered! • If 3 parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

  11. Example 3 y 16.5 15 25 x 30 x =18 y = 27.5

  12. Sail Making! • When making a boat sail, all of the seams are parallel. Find the missing variables • x = 2 ft, y=2.25 ft 1.5ft 2ft 1.5ft y x 1.5ft 3ft 2ft

  13. On your paper • Create a new triangle and label it ABC • Measure A • Bisect A by drawing an angle with half its measure. • Label the intersection point with the CB and the bisecting line point D • Compare the ratios of CD/DB and CA/BA • WHAT DID YOU NOTICE?

  14. Conclusion • If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle. • This is called the Triangle-Angle-Bisector Theorem.

  15. Example 4 • Set up the proportion • x=9.6 P 8 Q x 5 S R 6

  16. Homework • Work Book: Proportions and Similar Triangles

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