Use Side Lengths and Angle Measures to Draw and Analyze Triangles.pptx

draw triangle

1. Draw and Analyze Triangles Session 1

2. Give Me Five Use all the numbers in any order with any operation to equal the target number (in red).

3. In My Head? 25       How would you solve each problem – in your head, on paper, or with a calculator?

4. What do you notice? What do you wonder? Be Curious Mindset

5. What goal will you set for today's math class? What do you notice? What do you wonder? Be Curious Mindset

6. Marisa wants to use 3 of the 4 pieces of driftwood she found on the beach to construct a triangular border around a light post. Which pieces can Marisa use to construct the border? 4 Sticks, 1 Triangle

7. Marisa wants to use 3 of the 4 pieces of driftwood she found on the beach to construct a triangular border around a light post. Which pieces can Marisa use to construct the border? What strategy could you use to solve this problem? Reveal : 4 Sticks, 1 Triangle

8. Marisa wants to use 3 of the 4 pieces of driftwood she found on the beach to construct a triangular border around a light post. Which pieces can Marisa use to construct the border? What strategy could you use to solve this problem? Reveal : You could use repeated reasoning to make triangles with the different side lengths. 4 Sticks, 1 Triangle

9. What tool could help you solve this problem? Reveal : 4 Sticks, 1 Triangle

10. What tool could help you solve this problem? Reveal : You could use interactive geometry software to experiment with all the combinations to see if they can form triangles. 4 Sticks, 1 Triangle

11. Which sets of sides can be used to make a triangle? Let’s determine which sets of sides can be used to make a triangle. Begin with the 1-meter, 2-meter, and 3-meter-long sides. Collaborate and Connect Reveal :

12. Which sets of sides can be used to make a triangle? Let’s determine which sets of sides can be used to make a triangle. Begin with the 1-meter, 2-meter, and 3-meter-long sides. Collaborate and Connect Reveal : 1-meter, 2-meter, and 3-meter-long sides do not form a triangle.

13. Now, try the 1-meter, 2-meter, and 4-meter-long sides. Reveal : 4 Sticks, 1 Triangle

14. Now, try the 1-meter, 2-meter, and 4-meter-long sides. Reveal : 1-meter, 2-meter, and 4-meter-long sides do not form a triangle. 4 Sticks, 1 Triangle

15. Now try the 2-meter, 3-meter, and 4-meter-long sides. Reveal : 4 Sticks, 1 Triangle

16. Now try the 2-meter, 3-meter, and 4-meter-long sides. Reveal : 2-meter, 3-meter, and 4-meter-long sides do form a triangle. 4 Sticks, 1 Triangle

17. Now try the 2-meter, 3-meter, and 4-meter-long sides. Think About It : 4 Sticks, 1 Triangle

18. Now try the 2-meter, 3-meter, and 4-meter-long sides. Think About It : How do you know these are all the possible sets of sides? 4 Sticks, 1 Triangle

19. Think About It : 4 Sticks, 1 Triangle

20. Think About It : How do you know these are all the possible sets of sides? 4 Sticks, 1 Triangle

21. Marisa wants to use 3 of the 4 pieces of driftwood she found on the beach to construct a triangular border around a light post. Which pieces can Marisa use to construct the border? Marisa can use 2-meter, 3-meter, and 4-meter-long sticks to construct the border. Recognizing Repetition 4 Sticks, 1 Triangle

22. Marisa wants to use 3 of the 4 pieces of driftwood she found on the beach to construct a triangular border around a light post. Which pieces can Marisa use to construct the border? How can you use a pattern to make a rule? Marisa can use 2-meter, 3-meter, and 4-meter-long sticks to construct the border. Recognizing Repetition 4 Sticks, 1 Triangle

23. Workspace What conjectures can you make about the lengths of the sides of a triangle? Is it possible to make more than one triangle with the 2-meter, 3-meter, and 4-meter pieces of driftwood? Let’s Explore More Workspace

24. Draw and Analyze Triangles Session 2

25. What do you notice? What do you wonder? Be Curious Mindset

26. What are you doing to meet the goal you set for today’s math class? What do you notice? What do you wonder? Be Curious Mindset

27. Carlos has an assignment to create a design with one shape only. His shape is the right triangle shown. He can change only the side lengths and the color of the triangle, but not the angle measures. What might his design look like? Triangle Designs

28. Carlos has an assignment to create a design with one shape only. His shape is the right triangle shown. He can change only the side lengths and the color of the triangle, but not the angle measures. What might his design look like? What can vary in the triangles used for the design? Reveal : Triangle Designs

29. Carlos has an assignment to create a design with one shape only. His shape is the right triangle shown. He can change only the side lengths and the color of the triangle, but not the angle measures. What might his design look like? What can vary in the triangles used for the design? Reveal : The color of the triangles and the lengths of the sides can vary. Triangle Designs

30. What tools could help you solve this problem? Reveal : Triangle Designs

31. What tools could help you solve this problem? Reveal : You could use rulers and protractors to draw examples that will help you solve this problem. Triangle Designs

32. How can you use rulers and protractors to draw examples that will help you solve this problem? Collaborate and Connect Reveal :

33. How can you use rulers and protractors to draw examples that will help you solve this problem? Collaborate and Connect Reveal : You can make many triangles of different sizes with the same angle measures. Use a protractor to create the triangles so that they have angles of , , and .  

34. How can you use rulers and protractors to draw examples that will help you solve this problem? Collaborate and Connect Think About It :

35. How can you use rulers and protractors to draw examples that will help you solve this problem? Collaborate and Connect Think About It : What do you notice about triangles that have the same angle measures?

36. A set of 3 angle measures does not form a unique triangle because many different triangles can be formed from 3 angle measures. Triangle Designs

37. He could use 12 triangles of increasing size to make a spiral design. Each triangle has the same angle measures. Each triangle in the design is unique, because it is the only triangle that can be formed from its 3 side lengths. Looking for Patterns Triangle Designs

38. He could use 12 triangles of increasing size to make a spiral design. Each triangle has the same angle measures. Each triangle in the design is unique, because it is the only triangle that can be formed from its 3 side lengths. How is looking for patterns helpful in solving this problem? Looking for Patterns Triangle Designs

39. Carlos has an assignment to create a design with one shape only. His shape is the right triangle shown. He can change only the side lengths and the color of the triangle, but not the angle measures. What might his design look like? Although all the triangles have the same angle measures, each triangle has a different set of side lengths. Triangle Designs

40. One friend insists that two angle measures and one side length will form a unique triangle. Do you agree with this statement? Explain. Let’s Explore More Workspace

41. When only one triangle can be formed from a set of measures, we say that the measures create a unique triangle. Summarize: Draw and Analyze Triangles Three side lengths form a unique triangle Three angles form more than one unique triangle Three side lengths that do not form a triangle. Triangles made with the same side lengths can have different orientations, but they are the same triangle. More than one unique triangle can be made from three angle measures. The sum of the lengths of the two shorter sides must be greater than the length of the longest third side.

42. Isaiah makes mixed media collages from natural and recycled materials. His next project will include a triangular region formed by 2 curly sticks and the bottom of a 14-inch square canvas. Choose a question to answer. Question 1: What will be the measure of the angle formed by the shorter stick and the canvas if Isaiah places the sticks so that they form the tallest possible triangular region? Question 2: What will be the measure of the angle formed by the shorter stick and the canvas if Isaiah places the sticks so that they form the shortest possible triangular region? Apply: Mixed Media Canvas Art

43. I can draw triangles with given conditions. I can use repeated reasoning to determine the conditions that form a unique triangle, more than one triangle, or no triangle. Learning Targets