http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
Guidance
Same Side Interior Anglesare two angles that are on the same side of the transversal and on the interior of the two
lines.
Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior
angles are supplementary.
So, ifl||mand both are cut byt, thenm^63 +m^65 = 180 ◦andm^64 +m^66 = 180 ◦.
Converse of the Same Side Interior Angles Theorem:If two lines are cut by a transversal and the consecutive
interior angles are supplementary, then the lines are parallel.
Example A
Using the picture above, list all the pairs of same side interior angles.
Same Side Interior Angles:^6 4 and^6 6,^6 5 and^6 3.
Example B
Findm^6 2.
Here,m^61 = 66 ◦because they are alternate interior angles.^6 1 and^6 2 are a linear pair, so they are supplementary.
m^61 +m^62 = 180 ◦
66 ◦+m^62 = 180 ◦
m^62 = 114 ◦This example shows why if two parallel lines are cut by a transversal, the same side interior angles are supplementary.
Example C
Find the measure ofx.
The given angles are same side interior angles. The lines are parallel, therefore the angles add up to 180◦. Write an
equation.
( 2 x+ 43 )◦+( 2 x− 3 )◦= 180 ◦
( 4 x+ 40 )◦= 180 ◦
4 x= 140 ◦
x= 35 ◦Vocabulary
Same Side Interior Anglesare two angles that are on the same side of the transversal and on the interior of the two
lines. Two angles aresupplementaryif they add to 180◦.