CK-12 Geometry Concepts

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.