GEOMETRY: LOGIC

2-8: Proving Angle Relationships

DO NOW:

HOMEWORK

TODAY Angle Addition Relationships

Monday: Review

RECALL Angle Addition Postulate

RECALL Angle Addition Postulate:

m<ABD+ m<DBC = m< ABC

EXAMPLE 1 Given: m<1=56 and m<JKL=145Prove: m<1=89 2

1J

K

L

THEOREMS: Supplement Theorem: If two angles

form a linear pair, then they are supplementary angles.

THEOREMS Complement Theorem: If the

noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

EXAMPLE 2: Given: m<1=73 Prove: m<2=17

12

PROPERTIES Reflexive Property: <1<1

Symmetric Property: <1 <2 then <2 <1

Transitive Property: If <1 <2 and <2 <3 then <1 <3

THEOREMS: Congruent Supplements Theorem:

Angles supplementary to the same angle or to congruent angles are congruent themselves.

THEOREMS Congruent Complements Theorem:

Angles complementary to the same angle or to congruent angles are congruent themselves.

THEOREMS: Vertical Angles Theorem: If two angles

are vertical angles, then they are congruent.

EXAMPLE 3: Given: <1 and <2 are supplementary;

<2 and <3 are supplementary Prove: <1 <3

1 2

3

EXAMPLE 4: Given: bisects <ADC Prove: <2 <3

A

B

C

D

1 2

3

THEOREMS Perpendicular lines intersect to form

______________.

All right angles are ________________

Perpendicular lines form ____________ adjacent angles.

THEOREMS Perpendicular lines intersect to form

four right angles.

All right angles are congruent

Perpendicular lines form congruent adjacent angles.

THEOREMS CONTINUED If two angles are congruent and

supplementary, then each angle is ___________________

If two congruent angles form a linear pair, then they are ___________________

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.

EXAMPLE 5: Given: <5 <6 Prove: <4 and <6 are supplementary

5 4 6

PROVING THEOREMS: Prove that perpendicular lines intersect

to form four right angles.

PRACTICE PROBLEMS Try some on your own! As always call me over if you are

confused!

EXIT TICKET Given: <4 <7 Prove: <5 <6

4

5 6

7