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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)