Geometry – EOC Review
Chapter 3
Name: ________________________
Date: __________ Period: ________
Chapter 3 Concepts
Terms
∠1 and ∠3 are corresponding angles
∠2 and ∠6 are alternate interior angles
∠4 and ∠8 are alternate exterior angles
∠2 and ∠3 are same-side interior angles
∠1 and ∠4 are same-side exterior angles
Equations

(x1, y1) & (x 2, y 2 )
m=
Important theorems:
If two lines are parallel and are cut by a transversal
then:
corresponding, alternate interior, and alternate exterior
angles are congruent and same side interior and same
side exterior angles are supplementary.
If two lines are cut by a transversal and:
corresponding angles are congruent, alternate interior
angles are congruent, alternate exterior angles are
congruent, same side interior angles are supplementary
or same side exterior angles are supplementary
rise y 2 - y1
=
run x 2 - x1

Slope-Intercept form of an equation of a nonvertical line
y = mx + b, where m is the slope and b is the yintercept

Point-Slope form of an equation of a nonvertical line
y - y1 = m(x - x1), where m is the slope and
(x1, y1) is a point on the line.

If two non-vertical lines are perpendicular then
the product of their slopes is -1 (they are
opposite reciprocals of one another)
then the lines are parallel.
Two lines parallel to the same line are parallel to each
Slope Formula
The slope of a line containing the points
Constructions
other

Two lines perpendicular to the same line are parallel

Line parallel to given line through a point not on
the line
Line perpendicular to a given line through a
point on the line or a point not on the line
Use the diagram at the right to answer problems 1-4. Decide whether the angles are alternate interior angles,
same side interior angles, vertical, corresponding or alternate exterior angles.
1.
∠2 𝑎𝑛𝑑 ∠7
2.
∠1 𝑎𝑛𝑑 ∠4
3.
∠3 𝑎𝑛𝑑 ∠8
4.
∠7 𝑎𝑛𝑑 ∠4
Are the two lines in the diagram parallel? If so, explain how you know. If not, what information would be
needed to conclude the lines are parallel?
5. In the picture below 𝑖 ∥ 𝑗. Find the measure of the missing angles.
𝑚∠1 =
𝑚∠4 =
𝑚∠2 =
𝑚∠5 =
𝑚∠3 =
For problem 6- 8, find the value of x for which 𝑔 ∥ ℎ.
6.
7.
8.
For problems 9-10, find the value of each variable.
9.
10.
X=
X=
Y=
Z=
11. Given: 𝑙 ∥ 𝑚
Prove: ∠1 𝑎𝑛𝑑 ∠6 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦
Statements
Reasons
12. Which diagram below shows the first step in parallel line construction on a point outside a line.
13. What kind of line is being constructed in this series of diagrams?
14. Are lines m1 and m2 parallel?
Explain.
15. Are lines m1 and m2 perpendicular?
Explain.
16. Find the equation of the line that has a slope of 3 and passes through (1, -9). Put into slope intercept form.
17. Find the equation of the line that passes through (4, 2) and (3, -2). Put into slope intercept form.