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. Solution Not Possible Opener:
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.
Solution
Let x = the angle
then x = complement of the angle
and x = supplement of the angle
so x = x - 40
+x x
90 = 140 !
Not
Possible

3. What is true about AB and CD? What is true about AC and BD?
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. If FG ≅ HE, what can we say about FH and GE?
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. If the same segment is added to congruent segments,
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. If AB ≅ FG and BD ≅ GE, what do we know about AD and FE?
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. Proof: Theorem: If congruent segments are added to congruent segments,
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. If ABE ≅ DBC, what do we know about ABD and EBC? Why?
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. If the same angle is added to congruent angles,
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. If BAC ≅ GFH and CAD ≅ HFE, what else do we know? Why?
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. If congruent angles are added to congruent angles,
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. If FH ≅ GE, what can we say about FG and HE? Why?
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. If ABD ≅ EBC, what do we know about ABE and DBC? Why?
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. If the same segment (or angle) is subtracted from congruent
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. If AB ≅ FG and AD ≅ FE, what do we know about BD and GE? Why?
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. If BAC ≅ GFH and BAD ≅ GFE, what else do we know? Why?
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. If congruent segments (or angles) are subtracted from congruent
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. Using the Addition and Subtraction Properties in Proofs.
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.
Statement
Reason

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

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

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

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

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.

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

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