You will be able to use theorems and definitions to find the measures of angles. You will be able to use theorems and definitions to write a formal proof.
Indirect Proof – A proof that shows that the conclusion cannot be false because accepted facts would be contradicted.
Proof by contradiction (Indirect Proof) To prove: 4 and 6 are supplementary
Statement 1. n II m, transversal t 2. 4 and 6 are not supplementary 3. 4 + 6 180 o 4. 4 + o 5. n must intersect m This contradicts the given n II m Theorem is valid and proof is complete Reason 1.Given 2.Indirect proof assumption (something taken to be true without proof), the opposite of “To Prove”. 3.Def of angles that are not supplementary 4.Definition of not equal, greater than or less than 5.Euclid’s Postulate 5
1. n II m, transversal t 2. 4 + 6 = 180 o 3. 2 + 4 = 180 o 4. 4 + 6 = 2 + 4 5. 2 = 6 1.Given 2.Theorem, interior on the same side of the transversal are supplementary 3.Adjacent angles whose exterior sides are a straight line are supplementary. Definition of adjacent and supplementary. 4.Axiom 1, things equal to the same thing are equal to each other. 5.Axiom 3, equals subtracted from equals are equal. To Prove: 2 = 6
1. n II m, transversal t 2. 6 is supplementary to 2; 2 + 6 = 180 o 3. 4 + 6 = 180 o 4. 2 + 6 = 4 + 6 5. 2 = 4 To Prove: 2 = 4 1.Given 2.Definition of adjacent & supplementary 3.Theorem: interior angles on the same side of the transversal are supplementary 4.Axiom 1, things equal to the same thing are equal to each other. Steps 2 & 3 5.Axiom 3, equals subtracted from equals are equal.
If a transversal intersects two lines so that the alternate interior angles are equal, then the lines are parallel.
The m 7 is three times that of 6. 7 = 135 o ; 6 = 45 o. Eight times the m 5 = m 8. 5 = 20 o ; 8 = 160 o
Find the measure of the second angle: 1. One angle = 52 o o 2. One angle = 28 o o 3. One angle = 36 o o 4. One angle = 63 o o 5. One angle = 107 o 1.73 o
1 = 125 o 2 = 3 = 4 = 5 = 6 = 7 = 8 =