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Proportions in Triangles

Proportions in Triangles. Chapter 7 Section 5. Objectives. Students will use the Side-Splitter Theorem and the Triangle-Angle-Bisector Theorem. Question?. How do you know if two triangles are similar?. Remember.

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Proportions in Triangles

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  1. Proportions in Triangles Chapter 7 Section 5

  2. Objectives • Students will use the Side-Splitter Theorem and the Triangle-Angle-Bisector Theorem

  3. Question? • How do you know if two triangles are similar?

  4. Remember • When two or more parallel lines intersect other lines, proportional segments are formed.

  5. Side Splitter Theorem (7-4) • If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally (creates two proportional triangles).

  6. Turn to page 472… • Look at Problem 1 • Try the “Got It” problem for that example.

  7. Question • What condition of the Side-Splitter Theorem is marked in the diagram for Problem 1? • In other words, what is marked in the figure that lets us know we can use the Side-Splitter Theorem?

  8. Corollary to the Slide-Splitter Theorem • If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. A D E B C F

  9. On Page 473… • Look at Problem 2 • Try the “Got It” for this example

  10. Question: • Should the numerators and the denominators of each ratio in the proportion be corresponding sides of the figure?

  11. Triangle-Angle-Bisector Theorem (7-5) B • 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. A C D AD AB DC =CB

  12. On page 474 • Look at Problem 3

  13. Question • Using the diagram for Problem 3, and considering the properties of proportions, how can the proportion be rewritten so that the x is in a numerator?

  14. On page 474… • Try problems #1-8 on your own.

  15. Exit Slip/Reflection • What is the Side-Splitter-Theorem? • What is the Triangle-Angle-Bisector Theorem? • Give an example of each.

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