1. Lesson 2 – 8 Proving Angle Relationships
Geometry
Lesson 2 – 8
Proving Angle Relationships
Objective:
Write proofs involving supplementary angles.
Write proofs involving congruent and right angles.

2. Postulate 2.10 Protractor Postulate
Given any angle, the measure can be put into one-to-one correspondence with real numbers between 0 and 180.

3. Postulate 2.11
Angle Addition Postulate

4. Use Angle Addition Postulate
Find

5. Example If
Justify each step.
Angle Add. Post.
Sub
Sub
Subt. Prop.
Sub

6. Theorems Supplement Theorem Complement Theorem
If two angles form a linear pair, then they are supplementary angles.
Complement Theorem
If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

7. Example Angles 6 & 7 form a linear pair. 3x + 32 + 5x + 12 = 180
Justify each step.
Supplement Thm.
3x x + 12 = 180
Sub
8x + 44 = 180
Sub
8x =
Subt. Prop.
8x = 136
Sub
Division Prop.
x = 17
Sub

8. Properties of Angle Congruence
Reflexive
Symmetric
Transitive

9. Theorem Congruent Supplement Theorem Abbreviation:
Angles supplementary to the same angle or to congruent angles are congruent.
Abbreviation:

10. Theorem Congruent Complements Theorem Abbreviation
Angles complementary to the same angle or congruent angles are congruent.
Abbreviation

11. Prove that the vertical angles 2 and 4 are congruent.
Given:
Prove:

12. Theorem 2.8 Vertical Angle Theorem
If two angles are vertical angles, then they are congruent.

13. Prove that if DB bisects

14. Right Angle Theorems Theorem 2.9 Theorem 2.10 Theorem 2.11
Perpendicular lines intersect to form 4 right angles
Theorem 2.10
All right angles are congruent.
Theorem 2.11
Perpendicular lines from congruent adjacent angles.

15. Theorem 2.12
If two angles are congruent and supplementary, then each angle is a right angle.
Theorem 2.13
If two congruent angles form a linear pair, then they are right angles.

16. Homework
Pg – 4 all, 6, 8 – 14, all