Download Unit 3 Corrective

Name: ________________________ Class: ___________________ Date: __________
Geometry - Chapter 3 Corrective #1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine whether the lines 12x − 4y = −3 and y = x + 5 are parallel, intersect, or coincide.
a. parallel
c. coincide
b. intersect
____
2. Identify a pair of skew segments.
a.
b.
AB & EF
FB & AB
c.
d.
1
AB & HG
DH & FG
ID: A
____
3. In a swimming pool, two lanes are represented by lines l and m. If a string of flags strung across the lanes is
represented by transversal t, and x = 10, show that the lanes are parallel.
a.
b.
c.
d.
3x + 4 = 3(10) + 4 = 34°;
4x − 6 = 4(10) − 6 = 34°
The angles are alternate interior angles and they are congruent, so the lanes are parallel
by the Alternate Interior Angles Theorem.
3x + 4 = 3(10) + 4 = 34°;
4x − 6 = 4(10) − 6 = 34°
The angles are alternate interior angles, and they are congruent, so the lanes are parallel
by the Converse of the Alternate Interior Angles Theorem.
3x + 4 = 3(10) + 4 = 34°;
4x − 6 = 4(10) − 6 = 34°
The angles are corresponding angles and they are congruent, so the lanes are parallel by
the Converse of the Corresponding Angles Postulate.
3x + 4 = 3(10) + 4 = 34°;
4x − 6 = 4(10) − 6 = 34°
The angles are same-side interior angles and they are supplementary, so the lanes are
parallel by the Converse of the Same-Side Interior Angles Theorem.
Short Answer
4. Give an example of same side interior angles.
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5. Use the slope formula to determine the slope of the line. Show your work. NO work, NO credit.
6. Use the information m∠1 = (4x + 50)°, m∠2 = (8x − 10)°, and x = 15 , and the theorems you have learned to
show that j Ä k .
j
1
k
2
m
3
7. Graph the line y − 6 = 5(x − 3) .
8. Find m∠SUV .
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9. Identify the transversal and classify the angle pair ∠1 and ∠6.
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
____ 10. 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
____ 11. 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
____ 12. 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
____ 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 on
the same sides of the other two lines
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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
____ 15. y − y 1 = m(x − x 1 ) , where m is the slope and (x 1 , y 1 ) is a point on the line
____ 16. the length of the perpendicular segment from the point to the line
____ 17. the difference in the y-values of two points on a line
____ 18. the difference in the x-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
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
____ 21. lines that intersect at 90° angles
____ 22. a line perpendicular to a segment at the segment’s midpoint
____ 23. lines in the same plane that do not intersect
____ 24. planes that do not intersect
____ 25. lines that are not coplanar
6
ID: A
Geometry - Chapter 3 Corrective #1
Answer Section
MULTIPLE CHOICE
1. ANS: B
2. ANS: D
3. ANS: B
TOP: 3-6 Lines in the Coordinate Plane
TOP: 3-1 Lines and Angles
TOP: 3-3 Proving Lines Parallel
SHORT ANSWER
4. ANS:
∠8 and ∠4
TOP: 3-1 Lines and Angles
5. ANS:
7
−2
TOP: 3-5 Slopes of Lines
6. ANS:
By substitution, m∠1 = 3(20) + 30 = 90° and m∠2 = 5(20) − 10 = 90° .
By the Substitution Property of Equality, m∠1 = m∠2 = 90° .
By the Converse of the Alternate Interior Angles Theorem, l Ä m.
TOP: 3-3 Proving Lines Parallel
7. ANS:
TOP: 3-6 Lines in the Coordinate Plane
8. ANS:
m∠SUV = 72°
TOP: 3-2 Angles Formed by Parallel Lines and Transversals
1
ID: A
9. ANS:
The transversal is line m. The angles are alternate interior angles.
TOP: 3-1 Lines and Angles
MATCHING
10.
11.
12.
13.
14.
ANS:
ANS:
ANS:
ANS:
ANS:
B
F
G
E
C
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
15.
16.
17.
18.
19.
20.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
F
C
D
G
H
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
3-6 Lines in the Coordinate Plane
3-4 Perpendicular Lines
3-5 Slopes of Lines
3-5 Slopes of Lines
3-6 Lines in the Coordinate Plane
3-5 Slopes of Lines
21.
22.
23.
24.
25.
ANS:
ANS:
ANS:
ANS:
ANS:
C
E
A
B
D
TOP:
TOP:
TOP:
TOP:
TOP:
3-1 Lines and Angles
3-4 Perpendicular Lines
3-1 Lines and Angles
3-1 Lines and Angles
3-1 Lines and Angles
2