SAT Mc Graw Hill 2011

When Two Lines Cross

When two lines cross, four angles are formed.

“Vertical” angles are equal, and look like this:

Don’t be fooled by diagrams that look like ver-

tical angles, but aren’t. Vertical angles are

formed by two and only two crossed lines:

When two pairs of vertical angles are formed,

four pairs of adjacent angles (side-by-side) are

also formed. Adjacent angles add up to 180°:

When a Line Crosses Parallel Lines

Imagine taking two crossed lines, making a “copy” of
them, and sliding the copy down one of the lines so
that together they look like this:

This produces a pair of parallel lines crossed by a
third line.

"slide"

vertical not vertical

vertical

angles

CHAPTER 10 / ESSENTIAL GEOMETRY SKILLS 359

When two parallel lines are crossed by another

line, all acute angles are equal, and all obtuse

angles are equal. Also, every acute angle is sup-

plementary to every obtuse angle (that is, they

add upto 180 ).

To show that two lines are parallel, use the arrow

marks “>” like those in the figure in the previous

column. To show that two angles are equal, use

the arc marks “)” like those in the figure in the

previous column.

Don’t be fooled by diagrams that only look as

if they have two parallel lines crossed by an-

other line. Don’t assumethat two lines are par-

allel just because they lookparallel. It must be

giventhat they are parallel.

To help yourself to see the relationships be-

tween angles in parallel line systems, you

might try looking for these special “letters”:

Angles that make Z’s are equal:

Angles that make C’s or U’s are supplementary

(they have a sum of 180°):

Angles that make F’s are equal:

x°

x°

y° y°

b°

a°

a + b = 180 °

c° d°

c + d = 180 °

a°

a°

Lesson 1: Lines and Angles

adjacent angles