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.

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.

Postulate 2.11 Angle Addition Postulate

Use Angle Addition Postulate Find

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

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.

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

Properties of Angle Congruence Reflexive Symmetric Transitive

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

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

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

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

Prove that if DB bisects

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.

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.

Homework Pg. 154 1 – 4 all, 6, 8 – 14, 45 - 48 all