Download 2.2 Complementary and Supplementary Angles WK #2 THEOREMS

2.2 Complementary and Supplementary Angles
WK #2
THEOREMS and Examples
Date: ___________
These theorems and examples are not in textbook, but will be used for our class.
Be sure to learn them.
1. THEOREM :
Proof:
IF TWO ANGLES FORM A LINEAR PAIR , THEN
THE ANGLES ARE ____________________________
(Draw appropriate diagram)
Given: ∠ABD and ∠DBC are linear pairs
Prove:
Statements
Reasons
1. ∠ABD and ∠DBC are linear pairs 1.
2. ∠ABC is a straight angle
2.
3. m∠ABC = ________°
3.
4. ∠ABD is _________ to ∠DBC
4.
2. THEOREM :
IF THE NON-COMMON SIDES OF TWO ADJACENT
ANGLES ARE PERPENDICULAR, THEN
THE ANGLES ARE _____________________________.
Proof:
E
1
F
G
2
H
Given:
Prove:
Statements
1.
Reasons
1.
A
B
3. Given: Diagram as shown
2
Prove: ∠___ is supp to ∠____
1
3
4
D
Statements
Reasons
1.
1.
2.
2.
C
4. Be sure to set up each problem of this type following this model.
The measure of the supplement of an angle is 60 less than 3 times the
measure of its complement.
Find the measures of the angle, its supplement, and its complement.
Identify the variable and write expressions for the required angles first:
_____________ = measure of the angle
_____________ = measure of angle’s supplement
_____________ = measure of angle’s complement
Write an equation and solve:
5.)
a) Find x
E
D
3x + 40
20x + 30
B
2x + 30
A
C
⇒Fill in all measures in diagram
b) Find m∠ABC
c) Find m∠DBE
6. True or False:
________________
a. If two angles are linear pairs, they must be supplementary.
Diagram:
________________
b. If two angles are supplementary, they must be linear pairs.
Diagram:
7. Given: Diagram as shown,
∠1 is comp ∠2
A
Prove: AB ⊥ BC
(Note: This is problem 6 on p.69.
Our proof will be the preferred one
for our class.)
1
B
Statements
Reasons
1.
1.
2
C
Theorem: IF TWO _____________ ANGLES ARE ______________,
THEN THEIR NON-COMMON SIDES ARE ____________.
(If two ______________angles are _________________,
then they form __________________ lines)