Geometry Honors – Study Guide
Name ________________________ Pd ____
Chapter 3 – Parallel and Perpendicular Lines
3-1 Lines and Angles and 3-2 Properties of Parallel Lines
Definition
Symbol
Use the picture below:
Parallel Lines
Skew Lines
Parallel Planes
Coplanar
Parallel lines
are coplanar.
Which planes
contain ̅̅̅̅
𝑨𝑩?
Note: Sometimes you will need to visualize a plane that is
not shown in the picture.
Explain...
Definition
Name the line
Definition
Name the ∠𝒔
Transversal
Interior Angles
Exterior Angles
Alternate
Interior Angles
Same-Side
Interior Angles
Corresponding
Angles
Alternate
Exterior Angles
(Also called Consecutive Angles)
Special Angle Pairs w/ Parallel Lines
Definition
Interior Angles
Exterior Angles
Alternate Interior
Angles
Same-Side Interior
Angles
Corresponding
Angles
Alternate Exterior
Angles
Name the ∠𝒔
Postulate 3-1 –
Same-Side
Interior Angles
Postulate
If a transversal intersects two parallel lines,
then same-side interior angles are
supplementary.
Name the angles:
Theorem 3-1
Alternate
Interior Angles
Theorem
If a transversal intersects two parallel lines,
then alternate interior angles are congruent.
Theorem 3-2
Corresponding
Angles
Theorem
If a transversal intersects two parallel lines,
then corresponding angles are congruent.
Name the angles:
Name the angles:
Theorem 3-3
If a transversal intersects two parallel lines,
Alternate
then alternate exterior angles are congruent.
Exterior
Angles
Name the angles:
Theorem
Using the picture to the above right...
If m∠6 is 65º, then give the measures of the other angles and justify how you know this is true.
m∠2 is _______ because_________________________________________________________
m∠5 is _______ because _________________________________________________________
m∠8 is _______ because _________________________________________________________
m∠4 is _______ because__________________________________________________________
3-3 Proving Lines Parallel
Theorem 3-4 –
Converse of
the
Corresponding
Angles
Theorem
Theorem 3-5
Converse of
the Alternate
Interior Angles
Theorem
Theorem 3-6
Converse of
the Same-Side
Interior Angles
Postulate
Theorem 3-7
Converse of
the Alternate
Exterior
Angles
Theorem
If two lines and a transversal form
corresponding angles that are congruent,
then the lines are parallel.
If two lines and a transversal form alternate
interior angles that are congruent, then the
two lines are parallel.
If two lines and a transversal form sameside interior angles that are supplementary,
then the two lines are parallel.
If two lines and a transversal form alternate
exterior angles that are congruent, then the
two lines are parallel.
Proofs
-
Two-Column
Proof
Paragraph
Proof
Flow Proof
(see below)
Flow Proof
This includes arrows that show the logical connections between the
statements with the
reasons written below
the statements.
3-7 Equations of Lines in the Coordinate Plane
Slope
4 Main Slopes
of Lines
Slope Intercept
Form and
Point-Slope
Form
Forms of
Linear
Equations
Reminders:
How do you use the Slope-Intercept Form to graph a line?
How do you create a Point-Slope Form from 2 points?
How do you change a Point-Slope Form to a Slope-Intercept Form?
How do you find the slope or y-intercept from a standard equation of Ax + By = C?
3-4 Parallel and Perpendicular Lines and
3-8 Slopes of Parallel and Perpendicular Lines
Theorem 3-8 If two lines are parallel to the same line, then they are
parallel to each other.
Explain your thoughts:
Theorem 3-9
In a plane, if two lines are perpendicular to the same
line, then they are parallel to each other.
Explain your thoughts:
Theorem 310
In a plane, if a line is perpendicular to one of two
parallel lines, then it is also perpendicular to the other.
Explain your thoughts:
Slopes of Parallel Lines

If two nonvertical lines are parallel, then their slopes are ____________.

If the slopes of two distinct nonvertical lines are equal, then the lines are ________.

Any two vertical lines or horizontal lines are _____________.
Slopes of Perpendicular Lines

If two nonvertical lines are perpendicular, then the product of their slopes is ___________.

If the slopes of two lines have a product of -1, then the lines are ______________________.

Any horizontal lines and vertical line are ________________________.
3-5 Parallel Lines and Triangles
Postulate 3-2
Through a point NOT on a line, there is one and
Parallel
only one line parallel to the given line.
Postulate
Theorem 3-11
The sum of the measures of the angles of a
Triangle Angle- triangle is 180º.
Sum Theorem
Do the activity at the top of page 171.
Auxiliary Line
A line that you can add to a diagram to help
explain relationships in proofs.
Explain how ⃡𝑷𝑹 can help to prove that
𝒎∠𝑨 + 𝒎∠𝑩 + 𝒎∠𝑪 = 𝟏𝟖𝟎°?
Exterior Angle
of a Polygon
An angle formed by a side and an extension
of an adjacent side.
Remote
Interior Angles
The two nonadjacent interior angles to an
exterior angle of a triangle
Theorem 3-12
Triangle
Exterior Angle
Theorem
The measure of each exterior angle of a
triangle equals the sum of the measures of its
two remote interior angles.
𝒎∠𝟏 = 𝒎∠𝟐 + 𝒎∠𝟑