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Transcript

Is There a Bird in the Tree? Use the instructions below to create an origami Crane. 1. Begin with a square piece of paper. 2. Fold paper along the diagonal as shown. 3. Your crane should look like this. 4. Open the paper back up. Based on activities from Carnegie Learning 5. Fold both sides into the diagonal. 6. Your fold lines should look like this. Based on activities from Carnegie Learning 7. Fold the right half of the paper over the diagonal. 8. Fold the top flap of paper up. 9. Turn the paper over and fold the other flap of paper up. Based on activities from Carnegie Learning 10. Flip the paper back over. 11. Fold the top of the triangle back to form the crane’s neck. 12. Fold the top vertex forward to form the crane’s head. Based on activities from Carnegie Learning 13. Fold the bottom vertex up to form the crane’s tail. Voila! You now have an Origami Crane. Share it with all your friends!! 14. Now unfold your crane and trace all of the folding lines as shown. 15. Optional folds. Fold the corner in as shown. Based on activities from Carnegie Learning 16. Optional folds. Do the same to the other side. 17. Optional folds shown in red. Trace the new folding lines. 18. Your paper should now look like this. Optional folds shown in red. Based on activities from Carnegie Learning 19. Label the vertices of the triangles as shown. Optional folds shown in red. 20. How many triangles do you see being formed by the folds? 21. Name all of the triangles shown by the folds. 22. Consider ∆HSG. Classify the interior angles. a. The triangle can be classified as an acute triangle. Why? b. Can you find the sum of the measures of the three angles of this triangle without measuring? c. If so, what is the sum? If not, measure the angles to find the sum. d. Will the sum of the measures of the three angles of an acute triangle always be the same? Why or why not? 23. Consider ∆GFE, classify the interior angles. a. This triangle is known as a right triangle. Why? b. How many acute angles does it have? c. What is the sum of the measures of these acute angles? d. How do you know? Based on activities from Carnegie Learning e. Can you find the sum of the measures of the three angles of this triangle without measuring? f. If so, what is the sum? If not, measure the angles to find the sum. g. Will the sum of the measures of the three angles of a right triangle always be the same? Why or why not? 24. Consider ∆NCT; classify the interior angles of this triangle. a. This triangle is known as an obtuse triangle. Why? b. Can you find the sum of the measures of the three angles of this triangle without measuring? c. If so, what is the sum? If not, measure the angles to find the sum. d. Will the sum of the measures of the three angles of an obtuse triangle always be the same? Why or why not? 25. Are there any triangles in your diagram with exactly two congruent sides? If so, name them. If not, draw a triangle with exactly two congruent sides. a. This type of a triangle is called an isosceles triangle. An isosceles triangle is a triangle with at least two congruent sides. Measure the three angles. What do you notice? b. Do you think this is true for all isosceles triangles? 26. Are there any triangles in your diagram with three congruent sides? If so, name them. If not, draw a triangle with three congruent sides. a. This type of a triangle is called equilateral. Why? b. Measure the three angles of your equilateral triangle. What are their measures? c. What can you conclude about the three angles of an equilateral triangle? 27. If a triangle has three congruent angles, it is called equiangular. Why? a. What can you conclude about equiangular triangles? What can you conclude about equilateral triangles? 28. A scalene triangle is a triangle with no two sides congruent. Name all scalene triangles from your diagram. a. Measure the three angles of two of the scalene triangles. What do you notice? b. What can you conclude about the angle measures of a scalene triangle? 29. Is it possible to draw an isosceles right triangle? If so, draw it. If not, explain why not. 30. Is it possible to draw an isosceles obtuse triangle? If so, draw it. If not explain why not. 31. Is it possible to draw a scalene obtuse triangle? If so, draw it. If not, explain why not. 32. Is it possible to draw a scalene right triangle? If so, draw it. If not explain why not. Based on activities from Carnegie Learning 33. Is it possible to draw a scalene acute triangle? If so, draw it. If not, explain why not. 34. Is it possible to draw an equilateral obtuse triangle? If so, draw it, if not explain why not. 35. Can an isosceles triangle be equilateral? Why or why not? 36. Can an equilateral triangle be isosceles? Why or why not? 37. Can a right triangle be equilateral? Why or why not? Based on activities from Carnegie Learning Origami Crane Suggested Answers 1-19 create your crane, trace lines and label triangles. 20. 31. Answers may vary. 21. ∆ABM, ∆ABJ, ∆ACL, ∆BNM, ∆BNC, ∆BMJ, ∆COP, ∆CBN, ∆CPQ, ∆CNT, ∆CQR, ∆CTS, ∆CJE, ∆CRD, ∆CSE, ∆CHF, ∆ESG, ∆EGF, ∆EJF, ∆GSJ, ∆GHS, ∆HSJ, ∆IWJ, ∆ JWV, ∆JST, ∆ JVU, ∆JTN, ∆ JUK, ∆JNL, ∆ JMN, ∆ LMN 22. All are acute. a. Because all angles are acute. b. Yes. c. 180. d. Yes. Because the sum of the measures of the three angles of a triangle is equal to 180. 23. Two are acute, one is right. a. Because it has a right angle. b. two c. 90. d. Because there are 180 degrees in a triangle. The right angle is equal to 90. Therefore the other two angles must equal 90 because 180 -90 = 90. e. yes f. 180. g. Yes. Because the sum of the measures of the three angles of a triangle is equal to 180. 24. Two are acute, one is obtuse. a. Because it has an obtuse angle. b. Yes. c. 180 d. Yes. Because the sum of the measures of the three angles of a triangle is equal to 180. 25. Yes. ∆SEG, ∆MNB, ∆HSG. Answers may vary depending on the folds. a. Two of the angles have the same measures. b. Yes. 26. No. Answers may vary. a. Because it has three congruent sides. Equi means equal and lateral means sides. b. They each measure 60º. c. The three angles of an equilateral triangle are congruent. 27. Because it has three equal angles. Equi means equal and angular means angles. a. Equiangular triangles are also equilateral. Equilateral triangles are also equiangular. 28. Answers may vary. a. The three angles have different measures. b. The three angles of a scalene triangle have different measures. 29. Yes. Make the legs of the right triangle congruent. 30. Yes. Make the two sides forming the obtuse angle congruent. 31. Yes. Make the three sides different lengths. 32. Yes. Make the two legs different lengths. 33. Yes. Make the three angles acute and the three sides different lengths. 34. No. If it is equilateral, it is also equiangular. 35. No. An equilateral triangle must have three congruent sides. 36. Yes. An equilateral triangle is isosceles, because by definition an isosceles triangle has at least two congruent sides. 37. No. An equilateral triangle is also equiangular. Based on activities from Carnegie Learning