Using inductive reasoning and conjectures Student Activity Sheet 2; use with Exploring The language of geometry
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1 1. REINFORCE Find a geometric representation for the following sequence of numbers. 3, 4, 5, 6, 7, 2. What are the three undefined terms in geometry? 3. Write a description of a point. How are points labeled? 4. Write a description of a line. How are lines labeled? 5. What are two names for the line containing points A and E? Page 1 of 9
2 6. Describe the difference between a line and a line segment. 7. What is meant by the notations AE, AE, and AE? 8. Write a definition of ray. 9. How do you name a ray in geometry? What is the name of a ray with endpoint I and point J on the ray? 10. Write a definition of angle. 11. REINFORCE How are DBG and m DBG different? Page 2 of 9
3 12. Write a description of a plane in geometry. 13. What is the minimum number of points needed to determine a line? A plane? 14. REINFORCE a. Name two points in the room diagram that are collinear with points C and F. b. Point J is noncollinear with points H and K. Name another point that is noncollinear with points H and K. c. Points C, Q, and S are coplanar points. Name another point on the floor that is coplanar with C and Q. d. Points A, B, and F are noncoplanar with point C. Name another point in the room that is noncoplanar with A, B, and F. Page 3 of 9
4 15. Using the notations provided, complete the table by writing in the correct notation for each name and figure. AB BA AB BA AB BA AB BA Page 4 of 9
5 16. Using the angle names provided, label the angles in the diagram below. B EAF A ECD FEA FAE CBA DCA 17. Draw and label LM where L has coordinates (3,-2) and M has coordinates REINFORCE (-1,5). Page 5 of 9
6 18. REINFORCE Suppose A and B are complementary angles, m A = (3x + 5), and m B = (2x 15). Solve for x and then find m A and m B. 19. REINFORCE The measure of the supplement of an angle is 12 more than twice the measure of the angle. Find the measures of the angle and its supplement. 20. Write a definition for angle bisector, and then sketch an example. Page 6 of 9
7 21. What is a conjecture? 22. Use Patty Paper to construct an angle bisector and place several points along the angle bisector. Write a conjecture about the distance from each point on the angle bisector to each side of the angle. 23. Do you think the angle bisector conjecture you wrote applies to all angles or just the one on your Patty Paper? 24. Do you know for a fact that the angle bisector conjecture you wrote is true? Page 7 of 9
8 25. REINFORCE In the diagram, AB bisects FAE. BF = 5x and BE = x Solve for x. 26. REINFORCE Using Patty Paper, construct a 45 angle. Describe your method. 27. Use Patty Paper or a protractor to construct two perpendicular lines. Then REINFORCE construct the angle bisectors of each of the angles formed by the intersecting lines. What conjecture can you make based on your construction? Page 8 of 9
9 28. Below are several isosceles triangles. Construct the angle bisector of A on REINFORCE each triangle. Then write a conjecture about the angle bisector of the angle formed by the two congruent sides of an isosceles triangle. Page 9 of 9
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