Download Topic 1 Review

Topic 1
Review
TOPIC VOCABULARY
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Check Your Understanding
Choose the correct term to complete each sentence.
1. A ray that divides an angle into two congruent angles is a(n) ? .
2. ? are two lines that intersect to form right angles.
3. A(n) ? is a geometric figure drawn using a straightedge and a compass.
1-1 Points, Lines, and Planes
Quick Review
Exercises
A point indicates a location and has no size.
Use the figure below for Exercises 4–6.
A line is represented by a straight path that extends in two
opposite directions without end and has no thickness.
A plane is represented by a flat surface that extends
without end and has no thickness.
Points that lie on the same line are collinear points.
Name all the segments and rays in
the figure.
A
Segments: AB, AC, BC, and BD
>
>
>
>
>
>
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Rays: BA , CA or CB , AC or AB , BC , and BD
5. Name the intersection of
planes QRB and TSR.
6. Name three noncollinear
points.
Points and lines in the same plane are coplanar.
Segments and rays are parts of lines.
Example
4. Name two intersecting lines.
T
S
Q
R
C
D
A
B
Determine whether the statement is true or false.
Explain your reasoning.
7. Two points are always collinear.
>
>
8. LM and ML are the same ray.
D
B
C
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1-2 Measuring Segments
Quick Review
Exercises
The distance between two points is the length of the
segment connecting those points. Segments with the same
length are congruent segments. A midpoint of a segment
divides the segment into two congruent segments.
For Exercises 9 and 10, use the number line below.
P
24
H
2
0
22
4
9. Find two possible coordinates of Q such that
PQ = 5.
Example
10. Find the coordinate of the midpoint of PH.
Are AB and CD congruent?
C
28
A D
26
24
B
0
22
11. Find the value of m.
2
3m 1 5
AB = 0 -3 - 2 0 = 0 -5 0 = 5
4m 2 10
A
CD = 0 -7 - ( -2) 0 = 0 -5 0 = 5
B
C
12. If XZ = 50, what are XY and YZ?
AB = CD, so AB ≅ CD.
a18
a
X
Z
Y
1-3 Measuring Angles
Quick Review
Exercises
Two rays with the same endpoint form an angle. The
endpoint is the vertex of the angle. You can classify angles
as acute, right, obtuse, or straight. Angles with the same
measure are congruent angles.
Classify each angle as acute, right, obtuse, or straight.
13.
14.
Example
If mjAOB = 47 and mjBOC = 73, find mjAOC.
B
A
Use the diagram below for Exercises 15 and 16.
N
M
P
O
m∠AOC = m∠AOB + m∠BOC
= 47 + 73
= 120
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Topic 1 Review
C
Q
R
15. If m∠MQR = 61 and m∠MQP = 25, find m∠PQR.
16. If m∠NQM = 2x + 8 and m∠PQR = x + 22,
find the value of x.
1-4 Exploring Angle Pairs
Quick Review
Exercises
Some pairs of angles have special names.
Name a pair of each of the following.
r Adjacent angles: coplanar angles with a common side,
a common vertex, and no common interior points
17. complementary angles
r Vertical angles: sides are opposite rays
18. supplementary angles
r Complementary angles: measures have a sum of 90
19. vertical angles
r Supplementary angles: measures have a sum of 180
20. linear pair
r Linear pair: adjacent angles with noncommon sides as
opposite rays
Find the value of x.
Angles of a linear pair are supplementary.
21.
B
A
C
D
E
(3x 1 31)8
F
(2x 2 6)8
Example
E
Are jACE and jBCD vertical
angles? Explain.
A
No. They have only one set of sides
with opposite rays.
22.
B
C
D
3x8
(4x 2 15)8
1-5 Basic Constructions
Quick Review
Exercises
Construction is the process of making geometric
figures using a compass and a straightedge. Four basic
constructions involve congruent segments, congruent
angles, and bisectors of segments and angles.
23. Use a protractor to draw a 73° angle. Then construct an
angle congruent to it.
Example
Construct AB congruent to EF .
E
F
Step 1
Draw a ray with endpoint A.
25. Sketch LM on paper. Construct a line segment
congruent to LM. Then construct the perpendicular
bisector of your line segment.
M
L
A
26. a. Sketch ∠B on paper. Construct
an angle congruent to ∠B.
Step 2
Open the compass to the length of
EF . Keep that compass setting and
put the compass point on point A.
Draw an arc that intersects the ray.
Label the point of intersection B.
24. Use a protractor to draw a 60° angle. Then construct the
bisector of the angle.
b. Construct the bisector of your
angle from part (a).
A
B
B
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Topic 1
TEKS Cumulative Practice
Multiple Choice
Read each question. Then write the letter of the correct
answer on your paper.
1. Points A, B, C, D, and E are collinear. A is to the right of
B, E is to the right of D, and B is to the left of C. Which
of the following is NOT a possible arrangement of the
points from left to right?
A. D, B, A, E, C
C. B, D, E, C, A
B. D, B, A, C, E
D. B, A, E, C, D
5. Which construction requires drawing only one arc
with a compass?
A. constructing congruent segments
B. constructing congruent angles
C. constructing the perpendicular bisector
D. constructing the angle bisector
< >
6. What is the intersection of AC and plane Q?
A
2. Which postulate most closely resembles the Angle
Addition Postulate?
E
B
D
F. Ruler Postulate
Q
C
G. Protractor Postulate
H. Segment Addition Postulate
J. Area Addition Postulate
3. What is the coordinate of the point that is 14 the distance
from 20 to 4 on a number line?
H. point B
G. point Q
J. point D
7. If ∠A and ∠B are supplementary angles, what angle
relationship between ∠A and ∠B CANNOT be true?
A. 8
C. 16
A. ∠A and ∠B are right angles.
B. 9
D. 15
B. ∠A and ∠B are adjacent angles.
C. ∠A and ∠B are complementary angles.
4. Given: ∠A
What is the second step in constructing the
angle bisector of ∠A?
D
A
D. ∠A and ∠B are congruent angles.
8. Which geometric term is undefined?
F. plane
B
G. angle bisector
H. construction
C
>
F. Draw AD .
G. From points B and C, use the same compass setting
to draw arcs that intersect at D.
H. Draw a line segment connecting points B and C.
J. From point A, draw an arc that intersects the sides of
the angle at points B and C.
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F. point E
Topic 1 TEKS Cumulative Practice
J. opposite rays
9. The measure of an angle is 12 less than twice the
measure of its supplement. What is the measure of
the angle?
A. 28
C. 64
B. 34
D. 116
10. If m∠BDJ = 7y + 2 and m∠JDR = 2y + 7, find the value
of y.
B
K
J
D
Constructed Response
18. Copy the graph below. Find the midpoints of
two adjacent sides of the square. Connect the
perpendicular bisectors of the two adjacent sides.
What is the perimeter of the new square? Show
your work.
R
y
F. y = 3
G. y = 8
4
H. y = 5
2
J. y = 9
x
11. Which statement is true?
26 24
22
O
A. It is possible for three points to be noncoplanar.
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B. A plane containing two points of a line contains the
entire line.
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C. Complementary angles are congruent.
D. A straight angle has a supplement.
12. The measure of an angle is 78 less than the measure of
its complement. What is the measure of the angle?
13. The measure of an angle is one third the measure of its
supplement. What is the measure of the angle?
14. Y is the midpoint of XZ. What is the value of b?
2b 2 1
26 2 4b
Y
19. Suppose PQ = QR. Your friend says that Q is always
the midpoint of PR. Is he correct? Explain.
20. Why might it be useful to have more than one way to
name an angle?
Gridded Response
X
4
Z
15. The sum of the measures of a complement and a
supplement of an angle is 200. What is the measure of
the angle?
21. The bisector of obtuse ∠AOD goes through point C.
The bisector of ∠AOC goes through point B.
a. If m∠COD = 4x + 12, what is the measure of
∠BOC in terms of x? How do you know?
b. If m∠COD = 4x + 12 and m∠AOD = 120, what is
the value of x? How do you know?
22. In JK , JH = 4x - 15 and HK = 2x + 3, where H is
between J and K on JK .
a. If JK = 48, find the value of x.
b. Is H the midpoint of JK ? Explain.
16. In AB, the coordinate of point A is -4, and the
coordinate of point B is 6. What is the coordinate of a
point C such that C is 38 of the distance from point A to
point B?
< >
17. VW is the bisector of AY , and they intersect at E. If
EY = 3.5, what is AY ?
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