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Similar Right Triangles Dr. Jennifer L. Brown, 2013, Columbus State University,

Similar Right Triangles Dr. Jennifer L. Brown, 2013, Columbus State University, CRMC Summer Workshop (MCC9‐12.G.SRT.4; MCC9‐12.G.SRT.5). Part 1. Materials Needed. rectangular piece of paper ruler scissors colored pencils. Step 1: Draw a diagonal. Step 2: Draw an altitude.

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Similar Right Triangles Dr. Jennifer L. Brown, 2013, Columbus State University,

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  1. Similar Right Triangles Dr. Jennifer L. Brown, 2013, Columbus State University, CRMC Summer Workshop (MCC9‐12.G.SRT.4; MCC9‐12.G.SRT.5)

  2. Part 1

  3. Materials Needed • rectangular piece of paper • ruler • scissors • colored pencils

  4. Step 1: Draw a diagonal.

  5. Step 2: Draw an altitude.

  6. Step 3: Label the triangles. 1 9 2 8 5 7 3 6 4

  7. Step 4: Cut out the triangles. 1 9 2 8 5 7 3 6 4

  8. Step 5: Arrange the triangles using 1, 4, & 7. 1 1 9 2 2 8 5 7 3 3 6 4

  9. Questions How are the two smaller triangles related to the large triangle? Explain how you would show that the triangle that includes ∠8 is similar to the triangle that includes ∠5. Explain how you would show that the triangle that includes ∠5 is similar to the triangle that includes ∠2.

  10. Questions Write a proportion involving the two legs of the triangle that includes ∠2 and the triangle that includes ∠5. Measure the legs in centimeters (to the nearest tenth) and substitute the values. Cross-multiply. What did you notice? 21.6 cm 17.1 cm bottom leg 2 right leg 2 bottom leg 5 right leg 5 ____________ = ____________ 27.9 cm 22.0 cm

  11. 7. Could we find the lengths for the other sides without measuring? 1 27.9 cm 9 2 13.2 cm 8 35.3 cm 21.6 cm 21.6 cm 5 17.1 cm 7 22.0 cm 17.1 cm 3 6 4 27.9 cm

  12. B B B Z Z Z Y Y Y X X X A A A C C C 10 54o 91o 91o 10 12 6 6 91o 15 9 15 91o 9 54o 18 How Can Triangles Be Proven Similar? Similar () triangles have congruent () angles and proportional sides. Side – Side – Side (SSS) Angle – Angle (AA) Side – Angle – Side (SAS) A  X C  Z C  Z AB BC CA XY YZ ZX BC CA YZ ZX ___ ___ ___ ___ ___ = = = Dr. Jennifer L. Brown, 2013, Columbus State University, CRMC Summer Workshop

  13. B B B Z Z Z Y Y Y X X X A A A C C C 10 54o 91o 91o 10 12 6 6 91o 15 9 15 91o 9 54o 18 How Can Triangles Be Proven Similar? Similar () triangles have congruent () angles and proportional sides. Side – Side – Side (SSS) Angle – Angle (AA) Side – Angle – Side (SAS) Dr. Jennifer L. Brown, 2013, Columbus State University, CRMC Summer Workshop

  14. Part 2

  15. Directions • Draw a diagonal from the top left corner to the lower right corner. • Cut along the diagonal.

  16. Label ΔABC (as shown). • Label points D, E, F, & G. • Fold side BC up to meet point D. (Keep BC ⊥ to AB. ) • Label point E. • Draw segment DE. • Repeat step 5 but meet point F. • Label point G. • Draw segment FG. A E D G F B C

  17. A • Measure the length of AC, AB, and BC (in centimeters to the nearest tenth). • Measure the length of AG, AF, and FG. • Measure the length of AE, AD, and DE. E D G F B C

  18. Questions • What do you notice about the following lengths? • AGAF • AC AB Why?

  19. Questions • 2. What do you notice about the following lengths? • DEAE • BC AC Why?

  20. Questions • 3. What do you notice about the following lengths? • AGFG • AB DE Why?

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