Download geometry classwork lesson 1-4 measuring segments and angles

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GEOMETRY CLASSWORK LESSON 1-4
MEASURING SEGMENTS AND ANGLES
1) Find the lengths determined by the points on the number line.
a) HI= ____________________________
b)GI= _____________________ c) EG=
____________
2) On the number line below, plot points A and B so that AB  4
In questions 3-5, point A is between points C and T on CT . Sketch each figure and find the missing
lengths.
3)
4)
5)
6) What is the distance between  4 and 7 on a number line?
A. –11
B. —3
7) On the number line below, JL = KM.
C. 3
* D. 11
What is the coordinate of M?
A. 27
B. 36
* C. 51
D. 6
8) A and B are points on a number line. Which expression will always represent the distance between A and
B? a) A  B
b) A  B
c) A  B
d) A  B
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9) What is the distance between  30 and 18 on a number line?
A)  48
b)  12
c) 12
d) 48
10) What is the midpoint of PQ below?
a) 40
b) 41
c) 42
d) 43
11) Measure AB to the nearest millimeter
a) 10.3mm
b)100 mm
*c) 104mm
d) 108mm
12) LLL On the number line below, which points would be 28 units away from point B?
a) 33 and 13
b) -13 and 43
c) -43 and 13
d) -13 and 33
13) What is the midpoint of PQ below?
a) 4
b) 6
c) 8
d) 10
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3
14) To the nearest
a) 2
1
2
1
inch , what is the length of BD ?
4
b) 2
3
4
d) 3
c) 3
1
4
15) LLL Using the number line shown below, what is the distance between points C and B?
a) -6
b) -3
c) 3
d) 6
16) If EF  2x 12 , FG  3x 15 and EG  23 find the values of x, EF, and FG. The drawing is not to
scale.
E
F
G
a) x = 10, EF = 8, FG = 15
b) x = 3, EF = –6, FG = –6
c) x = 10, EF = 32, FG = 45
d) x = 3, EF = 8, FG = 15
17) If T is the midpoint of
find the values of x and ST. The diagram is not to scale.
S
T
U
9x
4x + 25
a) x = 5, ST = 45
b) x = 5, ST = 60
18) Which point is the midpoint of ?
A
B
c) x = 10, ST = 60
C
–8 –7 –6 –5 –4 –3 –2 –1
D
0
1
d) x = 10, ST = 45
E
2
3
4
5
6
7
8
a) D
b) B
c) not B, C, or D
d) C
19) A line segment on a number line has endpoints with coordinates –12 and 20.
What is the length of the segment?
F8
G 12
H 20
J 32
20) A line segment on a number line has endpoints with coordinates –12 and 20.
What is the length of the segment?
F8
G 12
H 20
J 32
21) A line segment on a number line has one endpoint of -12. The length of the segment is 32. Which of the
following are the possible coordinates of the other endpoint?
I. – 44
II. – 20
III. 20
IV. 44
F I and II
G I and III
H II and IV
J III and IV
22) BCR: Look at the figure below:
If the length of PR is 300, what is the length of PQ ?
23) BCR: Points P, Q, and R are collinear, with Q between P and R.
PQ  5 x  30; QR  3x  80; PR  10 x  20 What is the length of PR ?
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MEASURING ANGLES
24) 1. Which of the following letters represents the vertex in the following picture?
A. D and E
B. E and H
C. F and G
D. G only
25) What is the measure of the solid line angle depicted by the following figure?
E. H only
A. 90 degrees
B. 180 degrees
C. 225 degrees
D. 270 degrees
26) What is the measure of angle B in the following figure if angle A measures 135°?
E. 0 degrees
A. 40°
B. 45°
27) In the figure below, what is the value of x?
a) 40
b) 45
28) XY passes through the endpoint of GF
A. 1
*B. 2
C. 50°
D. 135°
c) 65
C. 3
E. 225°
d) 80
D.4
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29) If the degree measure of each angle shown above is decreased by y, the resulting angles will be
complementary. What is the value of y?
(A) 90
(B) 70
(C) 65
(D) 50
(E) 45
30) Jim is raising a flagpole. The angle between the pole and the ground is currently 37 0
How many more degrees must Jim rotate the flagpole to make it perpendicular to the ground?
a) 37 0
b) 530
c) 90 0
d) 1430
31) Point M is located on AB . What is the value of x?
* A. 18
B. 36
C. 90
32) In the triangle below, angles A and B may be classified as what type of angles?
* A. complementary
B. supplementary
C. linear
D. 180
D. right
33) What is the measure of ∠B in ABC ?
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A. 580
B. 1200
* C. 1220
D. 138 0
34) The measures of 2 angles are 46 0 and 44 0 . These are examples of which type of angles?
A. vertical angles
B. a linear pair
C. supplementary angles
* D. complementary angles
35) Janeka used a protractor to measure the angle formed by the light beam from the lighthouse shown in
the figure below. What is the most reasonable angle measure Janeka found?
* A. 19 0
B. 96 0
C. 1020
D. 1610
36) What is the measure of angle ABC?
a) 550
b) 70 0
37) What is the measure of the smallest angle shown below ?
c) 1100
d) 1450
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a) 23 0
b) 28 0
*c) 330
d) 380
38) Angle A and angle B are a linear pair. Angle A has a measure of 36 degrees. What is the measure of
angle B?
a) 36 0
b) 540
c) 1440
d) 3240
39) Which is the measure of  CGE ?
a) 530
b) 730
c) 1030
d) 130 0
40) What is the difference between the measurements of  ABC and  A'BC ' ?
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*a) 80
41) What kind of triangle is ABC ?
b) 120
c) 54 0
d) 1260
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A) scalene
42) If
b) Isosceles
and
a)64
c) right
, then what is the measure of
b) 12
d) equilateral
The diagram is not to scale.
c) 52
d) 76
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43)
bisects
,
,
. Find
a)61
b)45.75
. The diagram is not to scale.
c) 91.5
d) 66
44) Look at the figure below:
Angles ABC and ABD form a linear pair. What is the value of x?
A 12.5
B 13.75
C 25
D 50
45) Look at the figure below:
Angles ABD and ABC form a linear pair. What is the measure of angle ABD?
A 2.5°
B 8.75°
C 40°
D 65°
46) BCR: Look at the drawing below:
If
is the angle bisector of  PQS , what is the measure, in degrees, of  PQS ?
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47) BCR: Look at the drawing below:
If
is the angle bisector of  PQS , what is the measure, in degrees, of  PQS ?
48) “Two lines in a plane always intersect in exactly one point.” Which of the following best describes a
counterexample to the assertion above?
A coplanar lines
B parallel lines
C perpendicular lines
D intersecting lines
49) Which of the following is NOT one of the undefined terms of geometry?
A angle
B line
C point
50) In the diagram below, line OP lies on plane T and line MN lies on plane S.
What is the intersection of planes S and T?
*A. line MN
B. point Q
C. line OP
D plane
D. point M
51) If the pattern below continues, what fractional part of the figure will be unshaded in Stage 7?
a)
19
20
b)
23
24
*c)
27
28
d)
31
32
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52) In the figure below, which pair of points is coplanar with TR
A. points G and H
*B. points F and H
C. points H and U
D. points H and
53) Given the pattern of identical squares below, how many squares would appear in Figure 5?
A. 10
B. 12
54) Ll
Which is the intersection of MN and plane K?
* A. point J
B. ‘  HJI
*C. 15
C. FH
D. 2
D. GI
55) Each figure shown below is made from equilateral triangles whose sides measure 1 cm.
If the pattern continues, what will be the perimeter of Figure 6?
A. 12 cm
* B. 18 cm
C. 21 cm
D. 36 cm
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56) Which can be identified using all three points E, F, and G?
A. a ray
* B. a plane
C. a chord
D. a line segment
57) If the pattern below continues, how many small squares will be in Figure 8?
* A. 36
B. 33
C. 27
D. 22
58) Below are three figures made of hexagons.
If the pattern were to continue, how many hexagons would make up Figure 5?
A. 32
B. 49
* C. 81
D. 98
59) The figure below represents Pascal’s Triangle. The sum of the numbers in Row 1 is 1, the sum of Row 2
is 2, and the sum of Row 3 is 4.
If this pattern continues, what is the sum of the numbers in Row 7?
A. 10
B. 32
* C. 64
D. 128
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60) Use the figures below to answer question
How many of the small triangles would be in the fifth figure of the pattern?
A. 25
B. 36
* C. 50
D. 72
61) Use the sequence below to answer question --23, --18, --13, --8, --3, ?
What is the next term in the sequence above?
* A. 2
B. 3
C. 5
D. 8
62) What is the eight term in the sequence : 5 , 2 , -1 , -4 , -7 , …..
a)-31
b) -22
63) What is the next term in this sequence? 12,4,
a)
4
81
* b)
*c) -16
d) -10
4 4
, ,---?
3 9
4
27
c)
4
12
d)
12
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64) What is the sixth number in the geometric pattern below
a) 6
b) 15
c) 21
d) 55
65) Ll a rancher increased the number of horses he owned for each of the past five years. The number of
horses he owned each year is listed below. Using the pattern, how many horses will the rancher own in
year 6?
Year 1
3 horses
a) 13 horses
Year 2
36 horses
Year 3
311 horses
b) 36 horses
Year 4
18 horses
* c) 38 horses
Year 5
27 horses
d) 40 horses
Year 6
?
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66) Avari is making a quilt using the Arkansas Traveler Variation pattern. She starts with the block below.
To draw the pattern, Avari sketches a second block by rotating the first block 90-degrees clockwise about the
origin. Avari sketches two more blocks, each time rotating the previous block 90-degrees clockwise about
the origin. When she completes the four blocks, which pattern has Avari made?
a)
b)
c)
67) What is the 7th number in the pattern below?
A. 11
* B. 20
d)
C. 23
D. 30
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68) In which direction would the final arrow point in Figure 6 of the pattern below?
a)
b)
c)
d)
69) L Which of the following represent the next number in the sequence :1 , 2 , 6 , 24 , 120 , ….
a) 154
b) 480
c)600
d) 720
70)
If the pattern continues, how many total blocks are in step 5?
A) 9
b) 23
*c) 25
d) 30
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71) A pattern known as the set of pentagonal numbers is illustrated below. The number of points used is
the value of each figure. What is the value of the 6th figure?
a) 38
b) 41
*c) 51
d) 53
72) Y is between X and Z, XY  5.8 and YZ  12.4 . Find XZ
a) 20.4
b) 18.2
c)16.5
d) 14.3
73) L is the midpoint of MN , ML  2x  7 and LN  3x  3 . Find ML, LN, and MN
a) 27,27.54
b) 27,27.32
c)44,44,88
d) 47,47,94
74) PQ bisects ST at R. SR  3x  3 and ST  30 .Find x.
a) x  2
b) x  4
c) x  6
d) x  9
75) Classify  OMN as acute, right, straight, or obtuse
a)acute
b) right
c) obtuse
d) straight
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76) Tell whether this statement is sometimes, always, or never true. Identify the answer, and the sketch to
support it. If I is not the midpoint of HJ , then H,I, and J are collinear
a)
b)
c)
d) Cannot be determined
77) Identify the protractor that shows the measure of  PQR as 1200
a)
b)
c)
d)
78) S is in the interior of  PQR , m  PQS  87 0 , and m  SQR  330 . Find m  PQR
a) 1200
b) 105 0
c) 86 0
d) 54 0
0
1

0
79) TV bisects  STU . m  STV   x  8  and m  UTV  x  2 . Find m  STU
4

0
0
a) 10
b) 20
c) 30 0
d) 40 0
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80) m  DFG  2 x  6 and m  EFG  3x  11 , find the value of x.
0
a) 35
0
b) 37
c) 39
d) 41
81) Classify  HIJ as acute, right , straight , or obtuse.
a)acute
b) right
c) obtuse
d) straight
82)
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