1. Same Shape Triangles Teacher Page – the complete lesson is available at the page Teaching Trigonometry.Teaching Trigonometry http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/teachi ng/trig.htm 1

2. 10/29/14 This work by Southwest Washington Mathematics Common Core Consortium is licensed under a Creative Commons Attribution 4.0 International License.Southwest Washington Mathematics Common Core ConsortiumCreative Commons Attribution 4.0 International License This work by Southwest Washington Mathematics Common Core Consortium is licensed under a Creative Commons Attribution 4.0 International License.Southwest Washington Mathematics Common Core ConsortiumCreative Commons Attribution 4.0 International License Same Shape Ratios TG.4 Special Ratios of Right Triangles 2

3. 3 Practice Target Practice 6. Attend to precision. Practice 7. Look for and make use of structure.Practice 7. Look for and make use of structure 3

4. 4 Learning Target G-SRTc I can define trigonometric ratios and solve problems involving right triangles.  Identify and define the sine, cosine and tangent ratios in terms of the angles of the triangles.  Use similar triangles to justify trigonometric ratio.

5. Which side of Δ ABC is the hypotenuse? 5 Launch hypotenuse

6. Which side is opposite from angle B? 6 Launch hypotenuse opposite

7. Referring to angle B, what name would you give to side AC? 7 Launch hypotenuse opposite adjacent

8. 8 Launch  AB  BC  AC hypotenuse Referring to angle C, which side is the

9. Always, Sometimes, Never In all triangles, there is one hypotenuse. hypotenuse is opposite angle A. 9

10. Always, Sometimes, Never In any right triangle, the hypotenuse is the longest side the smallest side is opposite the smallest angle 10

11. Always, Sometimes, Never In this triangle, Angles B and C have the same opposite side. Angles B and C have the same hypotenuse. The side opposite angle B is the side adjacent to angle C 11

12. 12 ExploreExplore

13. Calculating ratios for similar triangles 13

14. Each student takes two triangles. Measure each side to the nearest tenths of a centimeter and enter in the worksheet. Write the ratios as fractions and use a calculator to estimate them to 3 decimal places. 14 Calculating ratios for similar triangles

15. Complete the worksheet including the mean values for each ratio to 2 decimal places. Stack your triangles as neatly as possible on top of each other and discuss their findings. All members of your team need to be prepared to share your ratios and your findings with the class. 15 Calculating ratios for similar triangles

16. Record our Ratios 16 (degrees) 20304045506070 opp hyp adj hyp opp adj

17. Graph the three ratios from our table Use 3 different colors. 17

18. 18 Debrief How are the patterns you observe in the table shown in the graph? What information do you get from the graph, but not the table? What information do you get from the table, but not the graph?

19. 19 5 3 1 2 4 Learning Target Did you hit the target? Practice 7. Look for and make use of structure Practice 7. Look for and make use of structure. Rate your understanding of the target from 1 to 5. 5 is a bullseye!

20. 20 Practice

21. 21 Find the ratios for angle M

22. 22 Find the ratios for angle M