http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
TABLE3.1:(continued)
Statement Reason
8.^65 ,^66 ,^6 7, and^6 8 are right angles Definition of right angle
9.n⊥m Definition of perpendicular lines
Theorem #1: If two lines are parallel and a third line is perpendicular to one of the parallel lines, it is also
perpendicular to the other parallel line.
Or, ifl||mandl⊥n, thenn⊥m.
Theorem #2:If two lines are perpendicular to the same line, they are parallel to each other.
Or, ifl⊥nandn⊥m, thenl||m. You will prove this theorem in the review questions.
From these two theorems, we can now assume that any angle formed by two parallel lines and a perpendicular
transversal will always be 90◦.
Example A
Findm^6 CT A.
First, these two angles form a linear pair. Second, from the marking, we know that^6 ST Cis a right angle. Therefore,
m^6 ST C= 90 ◦. So,m^6 CT Ais also 90◦.
Example B
Determine the measure of^6 1.
From Theorem #1, we know that the lower parallel line is also perpendicular to the transversal. Therefore,m^61 =
90 ◦.
Example C
Findm^6 1.
The two adjacent angles add up to 90◦, sol⊥m. Therefore,m^61 = 90 ◦.
Watch this video for help with the Examples above.
MEDIA
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CK-12 Foundation: Chapter3PerpendicularLinesB
Vocabulary
Two lines areperpendicularif they meet at a 90◦, orright, angle.