Name:
Date:
Chapter 3 Summary and Review problems
Block:
Summary:
Section 3.1: Identify Pairs of Lines and Angles:
1. Parallel Lines
• How do we label a pair of parallel lines?
• Name a pair of parallel lines from the diagram.
2. Intersection Lines
• Name a pair of intersecting lines from the diagram?
3. Perpendicular Lines
• Two lines are perpendicular if _____________________________________
• How do we label a pair of perpendicular lines?
• Name a pair of perpendicular lines from the diagram?
4. Skew Lines
• Two lines are skew if _______________________________________________
• Name a pair of skew lines from the diagram.
5. Parallel Plane
• Parallel planes are two planes that _____________________________________
• Name 2 parallel planes from the diagram.
6. Transversal
• Transversal is line that ___________________________
• Name the transversal in the diagram:
7. Corresponding Angles
• Two angles are ________________ if they ________________________
• Name a pair of corresponding angles from the diagram: _____ _______
8. Alternate Interior Angles
• Two angles are ________________ if they _________________
• Name 2 alternate interior angles on the diagram: ____ ______
9. Alternate Exterior Angles
• Two angles are _______________ if they __________________
• Name 2 alternate exterior angles on the diagram: _____ ______
10. Consecutive Interior Angles
• Two angles are _____________ if they ____________________
• Name 2 consecutive interior angles on the diagram: _____ _______
11. Consecutive Exterior Angles (optional)
• Two angles are _____________ if they ____________________
• Name 2 consecutive exterior angles on the diagram: _____ _______
Section 3.2: Use Parallel Lines and Transversals
Corresponding Angles Postulate
Alternate Exterior Angles Theorem
Alternate Interior Angles Theorem
Consecutive Interior Angles Theorem
Name:
Converse Theorems/Postulates
Date:
Chapter 3 Summary and Review problems
Block:
Corresponding Angles Converse
then the _____________are ________________.
Alternate Exterior Angles Converse
then the _____________ are _________________.
Alternate Interior Angles Converse
then the _____________ are _________________.
Consecutive Interior Angles Converse
then the _____________ are _______________.
Transitive Property of Parallel Lines
If ________ ____________ are _______________ to the _______ ___________,
then they are _______________ to _____________________
Section 3.4: Find and Use Slopes of Lines
1. Explain the slope of a non-vertical line.
2. List the four types of slopes of lines in the Coordinate Plane:
3. Slopes of Parallel Lines are ____________________________
What is the symbol used that means parallel? _______________
Find the slope for lines k1 and k2 then determine if they are parallel.
4. Slopes of Perpendicular Lines are _________________________
What is the symbol used that means perpendicular? ___________
Find the slope of line h then draw a perpendicular line to line h
Through point P.
Section 3.5: Write and Graph Equations of Lines
1. What is the slope-intercept form of the linear equation? ________________________
2. What is the standard form of the linear equation? _____________________________
3. What is the point-slope form of the linear equation? ___________________________
Section 3.6: Prove Theorems About Perpendicular Lines SKETCHES
1. If two lines intersect to form a linear pair of congruent angles, then
___________________________________________________________
2. If two lines are perpendicular, then they intersect to form
__________________________________________________________________
3. If two sides of adjacent acute angles are perpendicular, then the angles are
___________________________________________________________________
4. If a transversal is perpendicular to one of two parallel lines, then it is
_____________________________________________________________________
5. In a plane, if two lines are perpendicular to the same line, then they are
____________________________________________________________________
6. Based on the figure to the right, name the following:
a. A pair of parallel lines
c. A pair of perpendicular lines
d. Two parallel planes
b. A pair of skew lines
e. Two perpendicular planes
6. Classify each pair of angles (use the letter). Some letters may be used more than once.
a)
b)
c)
d)
e)
f)
g)
∠5 and ∠8 ____
∠3 and ∠7 ____
∠2 and ∠5 ____
∠4 and ∠6 ____
∠3 and ∠8 ____
∠3 and ∠5 ____
∠1 and ∠3 ____
A. Corresponding
B. Alternate Interior
C. Alternate Exterior
D. Consecutive Interior
E. Linear Pair
F. Vertical Angles.
7. Find the measure of the missing angles.
_______
m ∠1 =
_______
m∠2 =
_______
m ∠3 =
_______
m∠4 =
Is there enough information to prove that line p || line q? If so, state the theorem or postulate you would use.
8.
10.
9.
Find the measure of the missing angles.
Lines p and q are not parallel.
m∠1 ________
m ∠4 ________
m ∠2 ________
m ∠5 ________
m∠3 ________
p
60° 1
4 5
Find the value of x that makes lines m and n parallel.
11.
12.
13. Decide if the following pairs of lines are parallel, perpendicular or neither.
1
y=
− x+2
3
1
=
y
x −1
3
_______________
14.
y = −3
y = 2x
x=3
=
y 2x + 7
________________
________________
Find the slope of the line containing the given points:
( 1, − 4 )
and (1, 3)
m = _____________
( 3, − 2 )
and
( −1, − 4 )
m = _________________
( −3, 5)
and ( 6, 5 )
m = _____________
q
2 3
100°
Write an equation of the line that passes through the given point P and has the given slope m. Graph each line. Leave
your equation in any form.
15. P ( −3, 2); m =
Write an equation for a line with the given information:
17. Parallel to
passing through the point
16.
P (3, 1); m = -4
18. Perpendicular to
Graph the following lines. Show at least two points.
19.
20.
passing through
21.
22. Lines a and b are perpendicular. Find the value of x.
x = _____________
60⁰
(2X)0
a
b