GeometryLesson 2 – 8

Proving Angle Relationships

Objective:Write proofs involving supplementary angles.

Write proofs involving congruent and right angles.

Postulate 2.10

Protractor PostulateGiven 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 .1455621 JKLmandmifm

JKLmmm 21145561 m891m

ExampleIf .3,131231 ofmeasurethefindABCmandmJustify each step.

ABCmmmm 321 Angle Add. Post.

13139023 m Sub

1313113 m Sub

1131311133113 m Subt. Prop.

183 m Sub

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.

Angles 6 & 7 form a linear pair. Example

.7&,6,,1257&3236 mmxfindxmxmIfJustify each step.

18076 mm Supplement Thm.

3x + 32 + 5x + 12 = 180 Sub

8x + 44 = 180 Sub

8x + 44 - 44 = 180 - 44 Subt. Prop.

8x = 136 Sub

8

136

8

8x

Division Prop.

x = 17 Sub977

836

m

m

Properties of Angle Congruence

Reflexive

Symmetric

Transitive

11

12,21 thenIf

.31,32&21 thenIf

TheoremCongruent Supplement TheoremAngles supplementary to the same angle

or to congruent angles are congruent.

Abbreviation:

TheoremCongruent Complements TheoremAngles complementary to the same angle

or congruent angles are congruent.

Abbreviation

Prove that the vertical angles 2 and 4 are congruent.

Given: anglesverticalare4&2 Prove: 42

Theorem 2.8

Vertical Angle Theorem If two angles are vertical angles, then they

are congruent.

Prove that if DB bisects .32, thenADC

Right Angle Theorems

Theorem 2.9Perpendicular lines intersect to form 4 right

angles

Theorem 2.10All right angles are congruent.

Theorem 2.11Perpendicular 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