CK-12 Geometry - Second Edition

http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines

m^6 ABD+m^6 DBC= 180 ◦ Linear Pair Postulate

m^6 ABD=m^6 DBC The two angles are congruent

m^6 ABD+m^6 ABD= 180 ◦ Substitution PoE

2 m^6 ABD= 180 ◦ Combine like terms

m^6 ABD= 90 ◦ Division PoE

So, anytime a linear pair is congruent, the angles are both 90◦.

Example 1:Findm^6 CT A.

Solution: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◦.

Perpendicular Transversals

Recall that when two lines intersect, four angles are created. If the two lines are perpendicular, then all four angles
are right angles, even though only one needs to be marked with the square. Therefore, all four angles are 90◦.

When a parallel line is added, then there are eight angles formed. Ifl||mandn⊥l, isn⊥m? Let’s prove it here.