Download Geo - CH3 Prctice Test

Geo - CH3 Prctice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. Identify the transversal and classify the angle pair ∠11 and ∠7.
a. The transversal is line l. The angles are corresponding angles.
b. The transversal is line l. The angles are alternate interior angles.
c. The transversal is line n. The angles are alternate exterior angles.
d. The transversal is line m. The angles are corresponding angles.
2. Draw two lines and a transversal such that ∠1 and ∠2 are alternate interior angles, ∠2 and ∠3 are
corresponding angles, and ∠3 and ∠4 are alternate exterior angles. What type of angle pair is ∠1
and ∠4?
a.
∠1 and ∠4 are supplementary angles.
b.
∠1 and ∠4 are corresponding angles.
c.
∠1 and ∠4 are vertical angles.
d.
∠1 and ∠4 are alternate exterior angles.
____
3. Violin strings are parallel. Viewed from above, a violin bow in two different positions forms two
transversals to the violin strings. Find x and y in the diagram.
a. x = 10, y = 20
b. x = 20, y = 20
____
c. x = 0, y = 60
d. x = −10, y = 140
4. Use the Converse of the Corresponding Angles Postulate and ∠1 ≅ ∠2 to show that l Ä m.
a. ∠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.
____
____
b. ∠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.
c. ∠1 ≅ ∠2 is given. From the diagram, ∠1 and ∠2 are corresponding angles. So by
the Corresponding Angles Postulate, l Ä m.
d. By the Converse of the Corresponding Angles Postulate, ∠1 ≅ ∠2. From the
diagram, l Ä m.
5. Write and solve an inequality for x.
a. x > 2
b. x < 2
6. Write a two-column proof.
Given: t ⊥ l, ∠1 ≅ ∠2
Prove: m Ä l
c. x > 1
d. x < −2
Complete the proof.
Proof:
Statements
1. [1]
2. t ⊥ m
3. m Ä l
Reasons
1. Given
2. [2]
3. [3]
a. [1] t ⊥ l, ∠1 ≅ ∠2
[2] 2 intersecting lines form linear pair of ≅ ∠s → lines ⊥.
[3] 2 lines ⊥ to the same line → lines Ä.
b. [1] t ⊥ l, ∠1 ≅ ∠2
[2] 2 lines ⊥ to the same line → lines Ä.
[3] 2 intersecting lines form linear pair of ≅ ∠s → lines ⊥.
c. [1] t ⊥ l, ∠1 ≅ ∠2
[2] 2 intersecting lines form linear pair of ≅ ∠s → lines ⊥.
____
[3] Perpendicular Transversal Theorem
d. [1] t ⊥ l, ∠1 ≅ ∠2
[2] Perpendicular Transversal Theorem
[3] 2 lines ⊥ to the same line → lines Ä.
7. Milan starts at the bottom of a 1000-foot hill at 10:00 am and bikes to the top by 3:00 PM. Graph
the line that represents Milan’s distance up the hill at a given time. Find and interpret the slope of
the line.
a.
The slope is 200, so Milan traveled 200 feet per hour.
b.
The slope is
200
7 ,
so Milan traveled
200
7
feet per hour.
The slope is
1
200 ,
so Milan traveled
1
200
feet per hour.
The slope is
7
200 ,
so Milan travels
c.
d.
____
7
200
feet per hour.
8. 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.
¸Ô
a. ÏÔ Ê
c. ÔÏ ÊÁ x, y ˆ˜ | y = 3x − 20 , y ≠ −2 Ô¸
ÔÌÓ Ë
Ô˝˛
ÌÔ ÁË x, y ˆ˜¯|| y = 13 x − 4 , x ≠ 6 ˝Ô
¯
Ó
˛
b.
____
ÏÔ Ê ˆ
¸Ô
ÌÔ ÁË x, y ˜¯|| y = 13 x − 4 ˝Ô
Ó
˛
9. Graph the line y − 3 = 4(x − 6).
a.
b.
____
d. ÏÔ ÊÁ x,
ÔÌÓ Ë
¸Ô
y ˆ˜¯ | y = 3x − 20 , x ≠ −2 Ô˝
˛
c.
d.
10. Determine whether the pair of lines 12x + 3y = 3 and y = 4x + 1 are parallel, intersect, or coincide.
a. intersect
c. parallel
b. coincide
Numeric Response
11. Find the value of x so that m Ä n.
12. A right triangle is formed by the x-axis, the y-axis and the line y = −2x + 3. Find the length of the
hypotenuse. Round your answer to the nearest hundredth.
Matching
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
____
____
____
____
13. a line that intersects two coplanar lines at two different points
14. 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
15. 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
16. 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
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
____
____
____
____
17. y − y1 = m(x − x1), where m is the slope and (x1, y1) is a point on the line
18. the difference in the y-values of two points on a line
19. a line with slope m and y-intercept b can be written in the form y = mx + b
20. a measure of the steepness of a line
____
____
21. the length of the perpendicular segment from the point to the line
22. the difference in the x-values of two points on a line
Geo - CH3 Prctice Test
Answer Section
MULTIPLE CHOICE
1. ANS: A
To determine which line is the transversal for a given angle pair, locate the line that connects the
vertices.
Corresponding angles lie on the same side of the transversal l, on the same sides of lines n and m.
Feedback
A
B
C
D
Correct!
Alternate interior angles lie on opposite sides of the transversal, between two
lines.
To find which line is the transversal for a given angle pair, locate the line that
connects the vertices.
To find which line is the transversal for a given angle pair, locate the line that
connects the vertices.
PTS: 1
DIF: Average
REF: Page 147
OBJ: 3-1.3 Identifying Angle Pairs and Transversals
NAT: 12.3.3.g
TOP: 3-1 Lines and Angles
2. ANS: B
Step 1 Draw two lines m, n, and a
Step 2 ∠2 and ∠3 are corresponding
transversal p such that ∠1 and ∠2 are
angles. Corresponding angles lie on the
alternate interior angles. They should lie same side of the transversal p and on the
on opposite sides of the transversal p
same sides of lines m and n. Add ∠3 to
between lines m and n.
the drawing.
Step 3 ∠3 and ∠4 are alternate exterior
angles. They should lie on opposite sides
of the transversal p and outside lines m
and n. Add ∠4 to the drawing.
∠1 and ∠4 are corresponding angles.
They lie on the same side of the
transversal p and on the same sides of
lines m and n.
Feedback
A
B
C
D
Angles 2 and 3 are corresponding angles and should lie on the same side of
transversal p, on the same sides of lines m and n.
Correct!
Angles 2 and 3 are corresponding angles and should lie on the same side of
transversal p, on the same sides of lines m and n.
Angles 1 and 2 are alternate interior angles and should lie on opposite sides of
transversal p, between lines m and n.
PTS: 1
DIF: Advanced
NAT: 12.2.1.f
KEY: multi-step
3. ANS: A
By the Corresponding Angles Postulate, (4x + y)° = 60°.
By the Alternate Interior Angle Postulate, (8x + y)° = 100°.
TOP: 3-1 Lines and Angles
8x + y = 100
−(4x + y) = −60
Subtract the first equation from the second.
4x = 40
x = 10
8(10) + y = 100
y = 20
Divide both sides by 4.
Substitute 10 for x.
Simplify.
Feedback
A
B
C
D
Correct!
When solving a system of two equations, subtract the second equation from the
first.
Use postulates related to parallel lines to form two equations.
When solving a system of two equations, subtract the second equation from the
first.
PTS: 1
NAT: 12.3.3.g
4. ANS: B
DIF: Advanced
REF: Page 157
OBJ: 3-2.3 Application
TOP: 3-2 Angles Formed by Parallel Lines and Transversals
∠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.
Feedback
A
B
C
D
Use the Converse of the Corresponding Angles Postulate.
Correct!
Use the Converse of the Corresponding Angles Postulate.
Use the given information.
PTS:
OBJ:
NAT:
5. ANS:
1
DIF: Basic
REF: Page162
3-3.1 Using the converse of the Corresponding Angles Postulate
12.3.3.g
TOP: 3-3 Proving Lines Parallel
A
DA > DC
DC is the shorter segment.
Substitute 2x + 4 for DA and 8 for DC.
2x + 4 > 8
Subtract 4 from both sides.
2x > 4
Divide both sides by 2 and simplify.
x>2
Feedback
A
B
C
D
Correct!
Change the inequality sign.
Check your simplification methods.
Do not change the inequality sign when subtracting 4 or dividing by 2.
PTS:
OBJ:
TOP:
6. ANS:
Proof:
1
DIF: Average
REF: Page 172
3-4.1 Distance From a Point to a Line
3-4 Perpendicular Lines
A
Statements
1. t ⊥ l, ∠1 ≅ ∠2
2. t ⊥ m
3. m Ä l
NAT: 12.3.5.a
Reasons
1. Given
2. If 2 intersecting lines form linear pair
of ≅ ∠s → lines ⊥.
3. If 2 lines ⊥ to the same line → lines Ä.
Feedback
A
B
C
D
Correct!
Switch Reason 2 and Reason 3.
Reason 2 is if 2 intersecting lines form a linear pair of congruent angles, then the
lines are perpendicular. Reason 3 is if 2 lines are perpendicular to the same line,
then the lines are parallel.
Reason 2 is if 2 intersecting lines form a linear pair of congruent angles, then the
lines are perpendicular. Reason 3 is if 2 lines are perpendicular to the same line,
then the lines are parallel.
PTS: 1
DIF: Basic
OBJ: 3-4.2 Proving Properties of Lines
7. ANS: A
REF: Page 173
NAT: 12.3.5.a
TOP: 3-4 Perpendicular Lines
Convert 3:00 pm to 15:00. Use the points (10, 0) and (15, 1000) to make the graph and find the
slope.
m=
1000 − 0
15 − 10
=
1000
5
= 200
The slope is 200, which means Milan is traveling at 200 feet per hour.
Feedback
A
B
C
D
Correct!
Convert 3:00pm to 15:00, then solve for the slope.
The slope is the distance traveled divided by the time elapsed.
Convert 3:00pm to 15:00, then solve for the slope.
PTS: 1
NAT: 12.3.5.a
8. ANS: A
DIF: Average
REF: Page 183
TOP: 3-5 Slopes of Lines
OBJ: 3-5.2 Application
−3 − (−5)
= 2 =− 1
−2 − 4
−6
3
y − (−2) y + 2
=
slope of CD =
,x≠6
6−x
6−x
Parallel lines have the same slope. Write an equation
y+2
= −1
6−x
3
comparing the slopes of AB and CD.
−3(y + 2) = 1(6 − x) Cross multiply.
−3y − 6 = 6 − x
Distribute.
−3y = 12 − x
Simplify.
slope of AB =
y = 13 x − 4
ÏÔ
ˆ˜| y = 1 x − 4 , x ≠ 6 ¸Ô˝.
y
3
Ô˛
Ó Ë ¯|
The set of possible values for x and y is ÔÌÔ ÊÁ x,
Feedback
A
Correct!
B
C
D
Check the constraints of x.
In the slope formula, the difference of the y-values is in the numerator and the
difference of the x-values in the denominator.
First, find the slopes of the segments. Then, set the slopes equal to each other
and cross multiply and simplify.
PTS: 1
DIF: Advanced
NAT: 12.3.3.g
9. ANS: B
The equation is given in point-slope form y − y1 = m(x − x1).
TOP: 3-5 Slopes of Lines
The slope is m = 4 = 41 and the coordinates of a point on the line are (6, 3).
Plot the point (6, 3) and then rise 4 and run 1 to locate another point. Draw the line connecting the
two points.
Feedback
A
B
C
D
The equation is of the form y − b = m(x − a), so the graph passes through the
point (a, b).
Correct!
The equation is of the form y − b = m(x − a), so the graph passes through the
point (a, b).
The equation is of the form y − b = m(x − a), so the graph passes through the
point (a, b).
PTS: 1
DIF: Average
REF: Page 191
OBJ: 3-6.2 Graphing Lines
NAT: 12.3.5.a
TOP: 3-6 Lines in the Coordinate Plane
10. ANS: A
Solve the first equation for y to find the slope-intercept form. Compare the slopes and y-intercepts
of both equations.
12x + 3y = 3
3y = −12x + 3
y = 4x + 1
y = −4x +
1
The slope of the first equation is –4 and
The slope of the second equation is 4 and
the y-intercept is 1.
the y-intercept is .
1
The lines have different slopes, so they intersect.
Feedback
A
B
C
Correct!
Write both lines in slope-intercept form and compare.
Write both lines in slope-intercept form and compare.
PTS: 1
DIF: Average
OBJ: 3-6.3 Classifying Pairs of Lines
TOP: 3-6 Lines in the Coordinate Plane
REF: Page 192
NAT: 12.3.5.a
NUMERIC RESPONSE
11. ANS: 17
PTS: 1
DIF: Average
TOP: 3-3 Proving Lines Parallel
12. ANS: 3.35
PTS: 1
DIF: Advanced
TOP: 3-6 Lines in the Coordinate Plane
NAT: 12.2.1.f
NAT: 12.3.3.d
MATCHING
13. ANS:
TOP:
14. ANS:
TOP:
15. ANS:
TOP:
16. ANS:
TOP:
E
PTS:
3-1 Lines and Angles
F
PTS:
3-1 Lines and Angles
G
PTS:
3-1 Lines and Angles
B
PTS:
3-1 Lines and Angles
1
DIF:
Basic
REF: Page 147
1
DIF:
Basic
REF: Page 147
1
DIF:
Basic
REF: Page 147
1
DIF:
Basic
REF: Page 147
17. ANS:
TOP:
18. ANS:
TOP:
19. ANS:
TOP:
20. ANS:
B
PTS: 1
3-6 Lines in the Coordinate Plane
C
PTS: 1
3-5 Slopes of Lines
G
PTS: 1
3-6 Lines in the Coordinate Plane
H
PTS: 1
DIF:
Basic
REF: Page 190
DIF:
Basic
REF: Page 182
DIF:
Basic
REF: Page 190
DIF:
Basic
REF: Page 182
TOP:
21. ANS:
TOP:
22. ANS:
TOP:
3-5 Slopes of Lines
F
PTS: 1
3-4 Perpendicular Lines
D
PTS: 1
3-5 Slopes of Lines
DIF:
Basic
REF: Page 172
DIF:
Basic
REF: Page 182