## SAT SUBJECT TEST MATH LEVEL 1

## PLANE GEOMETRY

## CHAPTER 8 Lines and Angles

### PERPENDICULAR AND PARALLEL LINES

Two lines that intersect to form right angles are called ** perpendicular**. Two lines that never intersect are said to be

**. Consequently, parallel lines form no angles. However, if a third line, called a**

*parallel***, intersects a pair of parallel lines, eight angles are formed, and the relationships between these angles are very important.**

*transversal***Key Fact G5**

**If a pair of parallel lines is cut by a transversal that is perpendicular to the parallel lines, all eight angles are right angles.**

**Key Fact G6**

**If a pair of parallel lines is cut by a transversal that is not perpendicular to the parallel lines:**

• **Four of the angles are acute, and four are obtuse.**

• **All four acute angles are congruent.**

• **All four obtuse angles are congruent.**

• **The sum of the measures of any acute angle and any obtuse angle is 180**º**.**

**TIP**

The four acute angles all have the same measure, and the four obtuse angles all have the same measure.

**EXAMPLE 3:** In the figure below, what is the value of *a* + *b* + *c* + *d* ?

By KEY FACT G6, *c* and *d* each measure 40° and 65 + *a* = 180. Therefore, *a* = 115. Since vertical angles have equal measures, *b* is also 115, and so

*a* + *b* + *c* + *d* = 115 + 115 + 40 + 40 = 310.

The converse of KEY FACT G6 is also true. If in the figure below, *x* = *y*, then lines and *m* are parallel.