1. 2-8: Proving Angle Relationships
Geometry: Logic
2-8: Proving Angle Relationships

2. Do Now:

3. Homework

4. Today
Angle Addition Relationships
Monday: Review

5. Recall
Angle Addition Postulate

6. Recall
Angle Addition Postulate:
m<ABD+ m<DBC = m< ABC

7. Example 1
Given: m<1=56 and m<JKL=145
Prove: m<1=89 K 2 J 1 L

8. Theorems:
Supplement Theorem: If two angles form a linear pair, then they are supplementary angles.

9. Theorems
Complement Theorem: If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

10. Example 2:
Given: m<1=73
Prove: m<2=17 1 2

11. Properties Reflexive Property: <1≅<1
Symmetric Property: <1 ≅ <2 then <2 ≅ <1
Transitive Property: If <1 ≅ <2 and <2 ≅ <3 then <1 ≅ <3

12. Theorems:
Congruent Supplements Theorem: Angles supplementary to the same angle or to congruent angles are congruent themselves.

13. Theorems
Congruent Complements Theorem: Angles complementary to the same angle or to congruent angles are congruent themselves.

14. Theorems:
Vertical Angles Theorem: If two angles are vertical angles, then they are congruent.

15. Example 3:
Given: <1 and <2 are supplementary; <2 and <3 are supplementary
Prove: <1 ≅ <3 1 2 3

16. Example 4: Given: 𝐷𝐵 bisects <ADC Prove: <2 ≅ <3 B A C 1 2 D

17. Theorems Perpendicular lines intersect to form ______________.
All right angles are ________________
Perpendicular lines form ____________ adjacent angles.

18. Theorems Perpendicular lines intersect to form four right angles.
All right angles are congruent
Perpendicular lines form congruent adjacent angles.

19. Theorems Continued
If two angles are congruent and supplementary, then each angle is ___________________
If two congruent angles form a linear pair, then they are ___________________

20. Theorems Continued
If two angles are congruent and supplementary, then each angle is a right angle.
If two congruent angles form a linear pair, then they are right angles.

21. Example 5: Given: <5 ≅ <6
Prove: <4 and <6 are supplementary 6 5 4

22. Proving Theorems:
Prove that perpendicular lines intersect to form four right angles.

23. Practice Problems Try some on your own!
As always call me over if you are confused!

24. Exit Ticket
Given: <4 ≅ <7
Prove: <5 ≅ <6 5 6 4 7