Geometry

1
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
• 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.

Justify each step.
Supplement Thm.
3x 32 5x 12 180
Sub
8x 44 180
Sub
Subt. Prop.
8x 44 - 44 180 - 44
8x 136
Sub
Division Prop.
x 17
Sub
8
Properties of Angle Congruence

• Reflexive
• Symmetric
• Transitive

9
Theorem

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

10
Theorem

• Congruent Complements Theorem
• 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
• 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. 154 1 4 all, 6, 8 14, 45 - 48 all