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Advanced Geometry Section 2.5 Addition and Subtraction Properties

Advanced Geometry Section 2.5 Addition and Subtraction Properties Le arner Objective: Students will apply the addition and subtraction 
 properties of segments and angles. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Opener:

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Advanced Geometry Section 2.5 Addition and Subtraction Properties

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  1. Advanced Geometry Section 2.5 Addition and Subtraction Properties Learner Objective: Students will apply the addition and subtraction 
 properties of segments and angles.

  2. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Opener: If the complement of an angle is 40 less than the 
supplement of the angle, find the measure of the angle. Let x = the angle then 90 - x = complement of the angle and 180 - x = supplement of the angle Solution so 90 - x = 180 - x - 40 +x +x 90 = 140 ! Not Possible

  3. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. What is true about AB and CD? What is true about AC and BD? Then what conclusion can we draw?

  4. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. If FG ≅ HE, what can we say about FH and GE?

  5. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Theorem: If the same segment is added to congruent segments, then the sums are congruent. (Addition Property) Proof:

  6. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. If AB ≅ FG and BD ≅ GE, what do we know about AD and FE?

  7. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Theorem: If congruent segments are added to congruent segments, then the sums are congruent. (Addition Property) Proof:

  8. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. If ABE ≅ DBC, what do we know about ABD and EBC? Why?

  9. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Theorem: If the same angle is added to congruent angles, then the sums are congruent. (Addition Property) Proof:

  10. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. If BAC ≅ GFH and CAD ≅ HFE, what else do we know? Why?

  11. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Theorem: If congruent angles are added to congruent angles, then the sums are congruent. (Addition Property) Proof:

  12. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. If FH ≅ GE, what can we say about FG and HE? Why?

  13. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. If ABD ≅ EBC, what do we know about ABE and DBC? Why?

  14. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Theorem: If the same segment (or angle) is subtracted from congruent  segments (or angles), then the differences are congruent. (Subtraction Property) Proof:

  15. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. If AB ≅ FG and AD ≅ FE, what do we know about BD and GE? Why?

  16. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. If BAC ≅ GFH and BAD ≅ GFE, what else do we know? Why?

  17. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Theorem: If congruent segments (or angles) are subtracted from congruent  segments (or angles), then the differences are congruent. (Subtraction Property) Proof:

  18. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Using the Addition and Subtraction Properties in Proofs. 1. An addition property is used when the segments or 
 angles in the conclusion are greater then those in the 
 given information. 2. A subtraction property is used when the segments or 
 angles in the conclusion are smaller than those in the 
 given information.

  19. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Reason Statement

  20. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Reason Statement

  21. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Reason Statement

  22. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Reason Statement

  23. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Reason Statement

  24. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles. Assignment 2.5: 4-10

  25. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  26. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  27. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  28. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  29. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  30. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  31. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  32. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  33. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  34. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  35. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  36. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  37. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  38. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  39. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  40. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  41. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  42. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  43. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  44. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

  45. Learner Objective: Students will apply the addition and subtraction properties of sebments  and angles.

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