3. rectangular piece of paper ruler scissors colored pencils

9. 1.How are the two smaller triangles related to the large triangle? 2.Explain how you would show that the triangle that includes ∠ 8 is similar to the triangle that includes ∠ 5. 3.Explain how you would show that the triangle that includes ∠ 5 is similar to the triangle that includes ∠ 2.

10. 4.Write a proportion involving the two legs of the triangle that includes ∠ 2 and the triangle that includes ∠ 5. 5.Measure the legs in centimeters (to the nearest tenth) and substitute the values. 6.Cross-multiply. What did you notice? 21.6 cm 27.9 cm 17.1 cm 22.0 cm

11. 7. Could we find the lengths for the other sides without measuring? 21.6 cm 27.9 cm 17.1 cm 22.0 cm 35.3 cm 27.9 cm 21.6 cm 17.1 cm 13.2 cm

12. How Can Triangles Be Proven Similar? Similar (  ) triangles have congruent (  ) angles and proportional sides. Angle – Angle (AA) 91 o A B C 54 o X Z Y 91 o  A   X  C   Z Side – Side – Side (SSS) X Z Y 18 9 15 10 A B C 12 6 ABBCCA XYYZZX ___ ___ ___ == Side – Angle – Side (SAS) X Z Y 9 91 o 15 91 o A B C 10 6  C   Z BCCA YZZX ___ =

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

15. 1.Draw a diagonal from the top left corner to the lower right corner. 2.Cut along the diagonal.

16. E G F D 3.Label ΔABC (as shown). 4.Label points D, E, F, & G. 5.Fold side BC up to meet point D. (Keep BC ⊥ to AB. ) 6.Label point E. 7.Draw segment DE. 8.Repeat step 5 but meet point F. 9.Label point G. 10.Draw segment FG. A BC

17. E G F D 11.Measure the length of AC, AB, and BC (in centimeters to the nearest tenth). 12.Measure the length of AG, AF, and FG. 13.Measure the length of AE, AD, and DE. A BC