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Deductive Reasoning

This comprehensive guide dives into the fundamentals of geometry, focusing on the Angle Bisector and Midpoint Theorems. Discover definitions, postulates, and theorems that justify diagrammatic statements while enhancing your deductive reasoning skills. Engage in written exercises to firmly grasp the concepts and improve problem-solving techniques related to angle measures and segment relationships. This resource is perfect for students seeking to strengthen their understanding of geometric principles. Good luck with your studies!

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Deductive Reasoning

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

  2. 2.3 Written Exercises What definition, postulate, or theorem justifies the statement about the diagram. 1 2 3 4 mp 1 Definition of midpoint

  3. What definition, postulate, or theorem justifies the statement about the diagram. 1 2 3 4 2 Definition of Angle Bisector

  4. What definition, postulate, or theorem justifies the statement about the diagram. 1 2 3 4 3 Definition of Angle Bisector

  5. What definition, postulate, or theorem justifies the statement about the diagram. 1 2 3 4 4 Angle addition postulate

  6. What definition, postulate, or theorem justifies the statement about the diagram. 1 2 3 4 5 Definition of Midpoint

  7. What definition, postulate, or theorem justifies the statement about the diagram. 1 2 3 4 6 Midpoint Theorem

  8. What definition, postulate, or theorem justifies the statement about the diagram. 1 2 3 4 7 Angle Addition Postulate

  9. What definition, postulate, or theorem justifies the statement about the diagram. 1 2 3 4 8 BD + DC = BC Segment Addition Postulate

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

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

  12. Write the number that is paired with the angle bisector . C 11 ? 122 E 18 0 180 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 L M N Note that each number was on the same spot on the protractor.

  14. 12 C] What is the measure of the angles formed by their bisectors? 60 P 60 30 30 60 120 L M N 60 + 30 = 900

  15. 12 D] Explain how you could of known the answer to part C without measuring the angles. 60 P 60 30 30 60 120 L M N Half of each portion is half of the whole 1800.

  16. 13 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: Find LN. LX = 40 – 16 = 24 X Y N L 16 40

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

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

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

  20. 14 bisects and bisects and bisects . Sketch the diagram and find: R 720 N Z W S T

  21. 14 bisects and bisects and bisects . Sketch the diagram and find: 18 36 R 720 N Z 18 W 18 36 36 36 S T

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

  23. 15 What additional information would be needed to conclude ? K M L G N H

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

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

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

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

  28. 19 Skip

  29. 19 Complete the proof of Theorem 2-2. Given: is the bisector of Prove: Given is the bisector of 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.

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