1. Deductive Reasoning “The proof is in the pudding.”“Indubitably.” Je solve le crime. Pompt de pompt pompt." Le pompt de pompt le solve de crime!" 2.3 Written Exercises

2. What definition, postulate, or theorem justifies the statement about the diagram. Definition of midpoint 1 43 21 mp

3. What definition, postulate, or theorem justifies the statement about the diagram. Definition of Angle Bisector 2 43 21

4. What definition, postulate, or theorem justifies the statement about the diagram. Definition of Angle Bisector 3 43 21

5. What definition, postulate, or theorem justifies the statement about the diagram. 4 43 21 Angle addition postulate

6. What definition, postulate, or theorem justifies the statement about the diagram. 5 43 21 Definition of Midpoint

7. What definition, postulate, or theorem justifies the statement about the diagram. 6 43 21 Midpoint Theorem

8. What definition, postulate, or theorem justifies the statement about the diagram. 7 43 21 Angle Addition Postulate

9. What definition, postulate, or theorem justifies the statement about the diagram. 8 43 21 Segment Addition Postulate BD + DC = BC

10. ? 80 40 180 0 9 Write the number that is paired with the angle bisector. C E D Average the numbers to find the middle value.

11. ? 120 30 180 0 10 Write the number that is paired with the angle bisector. C E D Average the numbers to find the middle value.

12. ? 122 18 180 0 11 Write the number that is paired with the angle bisector. C E D Average the numbers to find the middle value.

13. 12 A] draw a pair of angles like below. B] measure each angle with a protractor. P NLM Note that each number was on the same spot on the protractor.

14. 12 P NLM 120 C] What is the measure of the angles formed by their bisectors? 60 30 60 60 + 30 = 90 0

15. 12 P NLM 120 60 30 60 D] Explain how you could of known the answer to part C without measuring the angles. Half of each portion is half of the whole 180 0.

16. 13 N The coordinate of points L and X are 16 and 40 respectively. N is the midpoint of and Y is the midpoint of LN. Sketch a diagram and find: L X 1640 Find LN. LX = 40 – 16 = 24 Y

17. 13 N The coordinate of points L and X are 16 and 40 respectively. N is the midpoint of. Sketch a diagram and find: L X 1640 Find the coordinate of N. 28 Why ? Average the values.

18. 13 N The coordinate of points L and X are 16 and 40 respectively. N is the midpoint of. Sketch a diagram and find: L X 1640 Find coordinate of Y. 28 Y 22

19. 13 N The coordinate of points L and X are 16 and 40 respectively. N is the midpoint of. Sketch a diagram and find: L X 1640 Find LY. 28 Y 22 22 – 16 = 6

20. 14 Z bisects and bisects and bisects. Sketch the diagram and find: W T S R 72 0 N

21. bisects and bisects and bisects. 14 Z Sketch the diagram and find: W T S R 72 0 N 36 18 36

22. 15 L GNH M K Suppose that M and N are midpoints of and respectively. Which segments are congruent?

23. 15 L GNH M K What additional information would be needed to conclude ?

24. 16 Suppose bisects And bisects What angles are congruent?

25. 16 What additional information would be needed to show that ?

26. 17 Given: What can you deduce from the given information. AE = DE CE = BE AC = DB

27. 18 Given: What can you deduce from the given information. CE = BE AC = DB AE = EC = DE = EB

28. 19 Skip

29. 19 Complete the proof of Theorem 2-2. Given: Prove: is the bisector of Given Def. of Angle Bisector Angle Addition Postulate Substitution Combine like terms CLT Division Prop. Of Equality

30. C’est fini. Good day and good luck.