Download Unit 3 Review

Name: ________________________ Class: ___________________ Date: __________
Geometry - Chapter 3 Review 15-16
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. Identify a pair of parallel segments.
a.
AB Ä EH
c.
AB Ä HG
b.
FB Ä AB
d.
DH Ä FG
2. Use the Converse of the Corresponding Angles Postulate and ∠1 ≅ ∠2 to show that l Ä m.
a.
b.
c.
d.
∠1 ≅ ∠2 is given. From the diagram, ∠1 and ∠2 are corresponding angles. So by the
Converse of the Corresponding Angles Postulate, l Ä m.
∠1 ≅ ∠2 is given. From the diagram, ∠1 and ∠2 are alternate interior angles. So by the
Converse of the Alternate Interior Angles Postulate, l Ä m.
By the Converse of the Corresponding Angles Postulate, ∠1 ≅ ∠2. From the diagram,
l Ä m.
∠1 ≅ ∠2 is given. From the diagram, ∠1 and ∠2 are corresponding angles. So by the
Corresponding Angles Postulate, l Ä m.
1
ID: A
Name: ________________________
ID: A
Short Answer
3. Give an example of corresponding angles.
4. Find m∠RST .
5. Find m∠1 in the diagram. (Hint: Draw a line parallel to the given parallel lines.)
2
Name: ________________________
ID: A
6. Use the slope formula to determine the slope of the line. Show your work. NO work, NO credit.
7. Graph the line y − 3 = 4(x − 6) .
3
Name: ________________________
ID: A
8. Write a two-column proof.
Given: m∠1 + m∠2 = 180°
Prove: l Ä m
Complete the proof.
Proof:
Statements
1. m∠1 + m∠2 = 180°
2. m∠1 = m∠3
3. m∠3 + m∠2 = 180°
4. l Ä m
Reasons
1. Given
2. [1]
3. Substitution (Steps 1 and 2)
4. [2]
9. Write and solve an inequality for x.
10. Find m∠1 in the diagram. (Hint: Draw a line parallel to the given parallel lines.)
4
Name: ________________________
ID: A
11. Write a two-column proof.
Given: t ⊥ l, ∠1 ≅ ∠2
Prove: m Ä l
Complete the proof.
Proof:
Statements
1. [1]
2. t ⊥ m
3. m Ä l
Reasons
1. Given
2. [2]
3. [3]
12. AB Ä CD for A(4, − 5), B(−2, − 3) , C(x, − 2), and D(6, y) . Find a set of possible values for x and y.
Matching
Match each vocabulary term with its definition.
a. parallel lines
b. parallel planes
c. perpendicular lines
d. skew lines
e. perpendicular bisector
f. perpendicular planes
g. angle bisector
____ 13. lines that are not coplanar
____ 14. planes that do not intersect
____ 15. lines that intersect at 90° angles
____ 16. a line perpendicular to a segment at the segment’s midpoint
____ 17. lines in the same plane that do not intersect
5
Name: ________________________
ID: A
Match each vocabulary term with its definition.
a. vertical angles
b. alternate interior angles
c. corresponding angles
d. supplementary angles
e. transversal
f. same-side interior angles
g. alternate exterior angles
____ 18. a line that intersects two coplanar lines at two different points
____ 19. for two lines intersected by a transversal, a pair of angles that are on the same side of the transversal and on
the same sides of the other two lines
____ 20. for two lines intersected by a transversal, a pair of angles that are on opposite sides of the transversal and
outside the other two lines
____ 21. for two lines intersected by a transversal, a pair of angles that are on opposite sides of the transversal and
between the other two lines
____ 22. for two lines intersected by a transversal, a pair of angles that are on the same side of the transversal and
between the two lines
Match each vocabulary term with its definition.
a. x-intercept
b. point-slope form
c. rise
d. run
e. y-intercept
f. distance from a point to a line
g. slope-intercept form
h. slope
____ 23. y − y 1 = m(x − x 1 ) , where m is the slope and (x 1 , y 1 ) is a point on the line
____ 24. the difference in the y-values of two points on a line
____ 25. a line with slope m and y-intercept b can be written in the form y = mx + b
____ 26. a measure of the steepness of a line
____ 27. the length of the perpendicular segment from the point to the line
____ 28. the difference in the x-values of two points on a line
6
ID: A
Geometry - Chapter 3 Review 15-16
Answer Section
MULTIPLE CHOICE
1. ANS: C
2. ANS: A
TOP: 3-1 Lines and Angles
TOP: 3-3 Proving Lines Parallel
SHORT ANSWER
3. ANS:
∠8 and ∠4
TOP: 3-1 Lines and Angles
4. ANS:
m∠RST = 72°
TOP: 3-2 Angles Formed by Parallel Lines and Transversals
5. ANS:
m∠1 = 135°
TOP: 3-4 Perpendicular Lines
6. ANS:
−2
TOP: 3-5 Slopes of Lines
7. ANS:
TOP: 3-6 Lines in the Coordinate Plane
1
ID: A
8. ANS:
[1] Vertical Angle Theorem
[2] Converse of the Same-Side Interior Angles Theorem
TOP: 3-3 Proving Lines Parallel
9. ANS:
x>2
TOP: 3-4 Perpendicular Lines
10. ANS:
m∠1 = 85°
TOP: 3-2 Angles Formed by Parallel Lines and Transversals
11. ANS:
[1] t ⊥ l, ∠1 ≅ ∠2
[2] 2 intersecting lines form linear pair of ≅ ∠s → lines ⊥.
[3] 2 lines ⊥ to the same line → lines Ä.
TOP: 3-4 Perpendicular Lines
12. ANS:
ÏÔÔ
¸ÔÔ
|
1
ÌÔ ÊÁË x, y ˆ˜¯ | y = 3 x − 4 , x ≠ 6 ˝Ô
ÔÓ
Ô˛
TOP: 3-5 Slopes of Lines
MATCHING
13.
14.
15.
16.
17.
ANS:
ANS:
ANS:
ANS:
ANS:
D
B
C
E
A
TOP:
TOP:
TOP:
TOP:
TOP:
3-1 Lines and Angles
3-1 Lines and Angles
3-1 Lines and Angles
3-4 Perpendicular Lines
3-1 Lines and Angles
18.
19.
20.
21.
22.
ANS:
ANS:
ANS:
ANS:
ANS:
E
C
G
B
F
TOP:
TOP:
TOP:
TOP:
TOP:
3-1 Lines and Angles
3-1 Lines and Angles
3-1 Lines and Angles
3-1 Lines and Angles
3-1 Lines and Angles
23.
24.
25.
26.
27.
28.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
C
G
H
F
D
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
3-6 Lines in the Coordinate Plane
3-5 Slopes of Lines
3-6 Lines in the Coordinate Plane
3-5 Slopes of Lines
3-4 Perpendicular Lines
3-5 Slopes of Lines
2