http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
- Using your protractor, measure all of the angles. What do you notice?
In this investigation, you should see thatm^61 =m^64 =m^65 =m^6 8 andm^62 =m^63 =m^66 =m^6 7.^61 ∼=^64 ,^65 ∼=
(^6) 8 by the Vertical Angles Theorem. By the Corresponding Angles Postulate, we can say 6 1 ∼= (^6) 5 and therefore
6 1 ∼= (^6) 8 by the Transitive Property. You can use this reasoning for the other set of congruent angles as well.
Example 1:Ifm^62 = 76 ◦, what ism^6 6?
Solution:^6 2 and^6 6 are corresponding angles andl||m, from the markings in the picture. By the Corresponding
Angles Postulate the two angles are equal, som^66 = 76 ◦.
Example 2:Using the measures of^6 2 and^6 6 from Example 2, find all the other angle measures.
Solution:Ifm^62 = 76 ◦, thenm^61 = 180 ◦− 76 ◦= 104 ◦because they are a linear pair.^6 3 is a vertical angle with
(^6) 2, som (^63) = 76 ◦. (^6) 1 and (^6) 4 are vertical angles, som (^64) = 104 ◦. By the Corresponding Angles Postulate, we know
6 1 ∼= (^65) , 6 2 ∼= (^66) , 6 3 ∼= (^6) 7, and 6 4 ∼= (^6) 8, som (^65) = 104 ◦,m (^66) = 76 ◦,m (^67) = 76 ◦, andm 6 104 ◦.
Alternate Interior Angles Theorem
Example 3:Findm^6 1.