1. Advanced Geometry
Section 2.7 Transitive and Substitution Properties
Learner Objective: Students will apply the transitive property of angles
 and segments, the substitution property, and the Vertical Angle
 Theorem.

2. Warm Up: Given FC bisects AFE EB bisects DEF Prove: AFE ≅ DEF C D B A
Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
Warm Up: A B C D
Given FC bisects AFE
EB bisects DEF
Prove: AFE ≅ DEF G F E

3. If A ≅ B, and B ≅ C, then what must be true about A and C?
Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem. C A B
If A ≅ B, and B ≅ C, then what must be true about A 
and C?

4. If angles (or segments) are congruent to the same angle (or segment)
Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
THEOREM
If angles (or segments) are congruent  to  the same 
 angle (or segment)
then the angles (or segments) are congruent.
 (Transitive Property)
THEOREM
If angles (or segments) are congruent  to congruent 
 angles (or segments)
then the angles (or segments) are congruent.
 (Transitive Property)

5. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
PROPERTY:
Substitution Property: If two things are equal, one 
 can be substituted for the other.

6. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

7. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

8. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

9. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

10. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

11. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

12. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
Homework:
pg. 97
#3-5, 10, 12,13

13. Advanced Geometry
Section 2.8 Vertical Angles
Learner Objective: Students will apply the transitive property of angles
 and segments, the substitution property, and the Vertical Angle
 Theorem.

14. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
DEFINITION
Two collinear rays that have common endpoints and 
extend in opposite directions are called OPPOSITE RAYS. C A B

15. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

16. Which pairs of angles are vertical angles?
Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
DEFINITION
Two angles are VERTICAL ANGLES if the rays forming the sides of one and the rays forming the sides of the 
other are opposite rays.
Which pairs of angles are
vertical angles? E A B C D
What must be true about vertical angle pairs?

17. What must be true about vertical angle pairs?
Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
What must be true about vertical angle pairs?

18. If two angles are vertical angles, then they are congruent.
Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
THEOREM
 If two angles are vertical angles,
  then they are congruent. E A B C D

19. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

20. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

21. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

22. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

23. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

24. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.
Assignment
pg. 102
# 4, 5, 10, 12, 13
2.Review: 4, 5, 7, 11-18, 20, 21, 32, 33, 35

25. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

26. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

27. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

28. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

29. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.

30. Learner Objective: Students will apply the transitive property of angles and segments, the 
 substitution property, and the Vertical Angle Theorem.