8004 side splitter 2014

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8004 side splitter 2014

  1. 1. GT Geom 3/11/14 • Turn in CW/HW from yesterday on the book shelf. • Pass out papers in the bin. If you turn something into me it should have a grade on when you get it back. If you don’t turn it in to me you don’t get a grade.
  2. 2. Given Prove RSPQ// QT SQ PT RP  R P T Q S
  3. 3. Objective •Students will prove and apply the side- splitter theorem and other similarity properties.
  4. 4. Side-splitter Theorem •A line parallel to one side of a triangle divides the other two sides proportionally
  5. 5. Use the side-splitter to solve for x and y: 6 18 x 6 y
  6. 6. Check It Out! Example 1 Find PN. Substitute in the given values. Cross Products Prop.2PN = 15 PN = 7.5 Divide both sides by 2. Use the Triangle Proportionality Theorem.
  7. 7. Example 2: Verifying Segments are Parallel Verify that . Since , by the Converse of the Triangle Proportionality Theorem.
  8. 8. Check It Out! Example 2 AC = 36 cm, and BC = 27 cm. Verify that . Since , by the Converse of the Triangle Proportionality Theorem.
  9. 9. Two Transversal Proportionality Corollary •Two or more parallel lines divide two transversals proportionally c d a b a b = c d
  10. 10. So, you might want to ask yourself:• Can I find x? • NO YOU MUST KNOW LINES ARE // x 3 5 9
  11. 11. Solve for x 5x 15 3x 4x
  12. 12. Triangle Angle-Bisector Theorem • If a ray bisects an angle of a triangle then it divides the opposite side into segments proportional to the other two sides
  13. 13. The previous theorems and corollary lead to the following conclusion.
  14. 14. Example 4: Using the Triangle Angle Bisector Theorem Find PS and SR. by the ∆  Bisector Theorem. x = 30 PS = x – 2 SR = x + 5 = 30 – 2 = 28 = 30 + 5 = 35

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