Download Geometry Fall Semester Review

Name: ________________________ Class: ___________________Date:_______________
ID: 2009-10
Geometry Fall Semester Review
1 Line l passes through ÊÁË 1, 1 ˆ˜¯ and ÁÊË −2, − 8 ˜ˆ¯ . Graph the line perpendicular to l that passes through ÊÁË −2, 2 ˜ˆ¯ .
2 Draw an example of the Alternate Interior Angles Theorem.
3 "If I am invited, then I will go." What is the underlined portion called in this conditional statement?
____
4 Which figure below is not a convex polygon?
F
G
H
J
5 Tell whether the lines through the given points are parallel, perpendicular, or neither. Explain.
Line 1: ÁÊË 2, 2 ˜ˆ¯ , ÁÊË −4, 5 ˜ˆ¯
Line 2: ÊÁË 4, − 9 ˆ˜¯ , ÊÁË −6, − 4 ˆ˜¯
6 What can you conclude about ∆EGF?
1
7 A building casts a shadow 168 meters long. At the same time, a pole 5 meters high casts a shadow 20 meters
long. What is the height of the building?
Identify all triangles in the figure that fit the given description.
8 scalene
9 isosceles
10 acute
11 obtuse
12 equilateral
13 State two postulates or theorems that can be used to conclude that ∆AOB ≅ ∆COD .
2
14 Name three points in the diagram that are not collinear.
15 Look at the set of dots below. Sketch the next figure, and predict the total number of dots in the 6th figure.
Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which
congruence postulate or theorem you would use.
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17 Find the midpoint of the segment with endpoints (–1, –6) and (–15, 8)
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18 The midpoint of QR is M ÊÁË −1, − 1 ˆ˜¯ . One endpoint is Q( − 8, 3). Find the coordinates of the other endpoint.
Find the value of x.
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20
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22 A play yard is 20 ft by 17 ft. A fence is to be built around the yard. How many feet of fencing will be
needed? If fencing costs $3.35 per foot, what will be the cost of the fence?
4
Solve:
23
25
x
=
29 16
24 If p Ä q, solve for x.
25 The product label glued to a box of fruit is 12 inches wide by 7 inches tall. Part of the company logo on the
label is a circle that has a diameter of 5 inches. An enlarged copy of the label, 14.4 inches by 8.4 inches, is
used on a larger box. What is the circumference of the circle in the enlarged company logo? Use 3.14 as an
approximation for π and round your answer to the nearest tenth of an inch.
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→
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26 In the figure (not drawn to scale), MO bisects ∠LMN, m∠LMO = (19x − 24) °, and m∠NMO = (x + 66)°.
Solve for x and find m∠LMN.
F
2, 20°
G
5, 142°
H
27 Write a definition for supplementary angles.
5
5, 119°
J
2, 29°
28 Explain why the figure shown does not satisfy the definition of a polygon.
29 State the postulate or theorem that can be used to prove that the two triangles are similar.
30 The two triangle-shaped gardens are congruent. Find the missing side lengths and angle measures.
31 The ratios of the side lengths of triangle ABC are 7:9:12 (AB:AC:BC). Solve for x.
32 Suppose ∆ABC ≅ ∆DEF, AB = 6 feet, m∠B = 65°, m∠F = 33°. True or false: ED = 6 ft.
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33 Tell whether lines m and n are parallel or not parallel and explain.
34 In the diagram, ∆ABC is similar to ∆EDC . Write the statement of proportionality.
35 Identify the congruent triangles. How do you know they are congruent?
36 Name a pair of vertical angles in the figure.
1
1
37 Are the lines with the equations y = − x + 2 and y = − x − 2 parallel, perpendicular, or skew?
3
3
7
38 Tell whether each pair of triangles is similar. Explain your reasoning.
39 Given that ∆ABC ∼ ∆DEF, solve for x and y.
40 Find the area and circumference of the circle. Use π = 3.14.
41 Solve for x, given that AB ≅ BC . Is ∆ABC equilateral?
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42 True or false: triangle ABC is similar to triangle DEF.
43 ∠1 and ∠2 form a linear pair. m∠1=73°. Find m∠2
44 A line is perpendicular to y =
x
− 2 and passes through point (6, 2). Write its equation.
3
45 Name an angle supplementary to ∠2 in the figure.
46 Sketch an example of lines intersected by a transversal. Label a pair of alternate interior angles.
47 ∆MNO and ∆EFG are similar with m∠M = m∠E and m∠N = m∠F . If MN, NO, and MO are 8 inches, 10
inches, and 11 inches respectively, and EF is 9.9 inches, find EG.
48 If ∆RPQ ≅ ∆JKL, then LJ ≅
.
9
49 Given: PQ || BC . Find the length of AP.
____
50 Which is the appropriate symbol to place in the blank? (not drawn to scale)
AB __ AC
F
G
>
=
H
J
51 Given AE Ä BD. Solve for x.
10
not enough information
<
52 Determine whether the figures are similar.
53 A survey indicated that 3 out of 7 doctors used brand X aspirin. If 3500 doctors were surveyed, how many
used brand X?
54 If the pattern were continued, what would be the ratio of the number of unshaded squares to the number of
shaded squares in the next figure in the pattern?
55 In ∆QRS, QR = 10, RS = 11, and SQ = 12. In ∆UVT, VT = 20, TU = 24, and UV = 24. State whether the
triangles are similar, and if so, write a similarity statement.
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→
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→
56 What do PQ and QP have in common?
11
57 Given that
ED EC
=
, find AB to the nearest tenth. The figure is not drawn to scale.
BA BC
58 Which pair of lines is parallel if ∠1 is congruent to ∠7?
59 Identify the congruent triangles. How do you know they are congruent?
60 Use the figure to find the measure of ∠1.
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61 Given: PQ || BC . Find the length of CQ.
62 True or False: Points D, J, and E are coplanar.
63 Given that
ED EC
=
, find AB to the nearest tenth. The figure is not drawn to scale.
BA BC
64 Find the slope of the line that passes through the points A (-1,5) and B (7,1).
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65 Use information in the figure below to find m∠D.
66 Are the two triangles (not drawn to scale) similar? If so, explain why they are.
67 If AB = 10 and AC = 24, find the length of BC.
68 Sketch a five-sided polygon that is convex.
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69 Find AB and BC in the situation shown below.
AB = x + 16, BC = 5x + 10, AC = 56
70 Classify ∆LMN as equilateral, isosceles, or scalene.
71 Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent?
72 Given the following statements, can you conclude that Becky plays basketball on Wednesday night?
(1) If it is Wednesday night, Becky goes to the gym.
(2) If Becky goes to the gym, she plays basketball.
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73 Name 4 pairs of perpendicular lines in the figure.
Use the table to decide whether inductive or deductive reasoning is used to reach the conclusion.
x
y
0
1
1
3
2
5
3
7
4
9
5
?
74 The values of y are found using the formula y = 2x + 1, when x = 0, 1, 2, 3, or 4.
75 Solve for x, given that AB ≅ BC . Is
ABC equilateral?
76 "If it doesn’t rain, then I will go to the game." What is the underlined portion called in this conditional
statement?
77 Find the distance between the points (–5, 9) and (–9, 12).
78 The measure of angle C is 78°. Classify angle C as an acute, right, or obtuse angle.
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79 m∠ECD = (2x + 6)° and m∠BCD = (10x − 5)° and m∠ECB = 61°.
Find m∠ECD and m∠BCD.
80 State the postulate or theorem that can be used to prove that the two triangles are similar.
81 Solve for x:
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→
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→
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→
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→
82 Draw four points, A, B, C, and D, on a line so that AC and AB are opposite rays and AC and AD are the
same ray.
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83 Find the area of the shaded figure.
84 Refer to the figure below. Give a reason to justify the statement.
∠CDO ≅ ∠COD
85 If AB = 12 and AC = 30, find BC.
86 Which lines, if any, can be proved parallel given the following diagram?
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87 At the same time of day, a man who is 70.5 inches tall casts a 36-inch shadow and his son casts a 24-inch
shadow. Use similar triangles to determine the height of the man's son. State the postulate or theorem that can
be used to prove the triangles are similar and then justify your answer.
88 What is the slope of a line parallel to the line 3x − 2y = 8?
89 State the postulate or theorem that can be used to prove that the two triangles are similar.
90 Define skew lines.
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ID: A
Geometry Fall Semester Review
Answer Section
1 Answer:
2 Answers vary.
Check art. Drawings should demonstrate that if two parallel lines are cut by a transversal, then the pairs of
alternate interior angles are congruent.
3 The conclusion
4 F
5 Parallel; the lines have the same slope.
6 ∆EGF is equilateral and equiangular.
7 42 meters
8 ∆ABD
9 ∆ACB, ∆ACD
10 ∆ACD
11 ∆BAC
12 ∆ACD
13 SAS and SSS Congruence Postulates
14 Answers will vary. P, V, and R
15
16
17
18
19
45
yes; SSS Postulate
(–8, 1)
(6, –5)
115
1
ID: A
20 40
21 18
22 74 ft; $247.90
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23 13
29
24 15
25 18.8 inches
26 G
27 Two angles are supplementary if the sum of their measures is 180°.
28 Not all sides are line segments.
29 AA Similarity Postulate
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
d = 56; e = 90; f = 34; c = 377 ; a = 19; b = 4
6
True
parallel; Corresponding Angles Converse
EC DC DE
=
=
BA
AC BC
∆WXZ ≅ ∆WYZ; SSS
∠1 and ∠3 or ∠2 and ∠4
parallel; Slopes are equal and y-intercepts are different
Yes; The two right angles are congruent, and since parallel lines are given the alternate interior angles are
congruent, so the triangles are similar by the AA Similarity Postulate
x = 8.57, y = 9.8
Area: 153.86 square units, Circumference: 43.96 units
x = 5; yes
true
107°
y = −3x + 20
∠1 or ∠3
Check students' sketches; example: the edges of the individual blinds in a set of mini-blinds and the rod used
to open them.
13.6 in.
QR
10
J
6
The figures are similar.
1500 used brand X
8
9
not similar
All of the points on PQ
13.9
2
ID: A
65
66
67
68
c and d
∆MNO ≅ ∆PRO; AAS
41°
21
True
16.9
1
−
2
41°
Yes; corresponding angles are equal in measure and ratios of corresponding sides are all equal.
14
Sketches may vary.
69
70
71
72
AB = 21, BC = 35
isosceles
SAS
yes
73
74
75
76
77
78
79
80
81
82
Sample answer: AB and BC , AB and AD , FG and GH , EC and EC
deductive
x = 8; no
The hypothesis
5 units
acute
m∠ECD = 16° and m∠BCD = 45°
AA Similarity Postulate
3
Sketches vary.
58
59
60
61
62
63
64
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←
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→ ←
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←
→ ←
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→
←
→ ←
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←
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83
9 square meters
84 If two sides of a triangle are congruent, then the angles opposite them are congruent.
85 18
86 No lines can be proved parallel from the given information.
3
ID: A
87 The son's height is 47 inches.
Reasons may vary: Since the triangles formed by the boy's respective height and shadow and the triangle
formed by his father's respective height and shadow are both right triangles with a pair of congruent acute
angles, you can apply the AA Similarity Postulate to conclude the two triangles are similar.
Son’s height
Son’s shadow
Ratios of lengths of corresponding
=
Father’s shadow Father’s height
sides are equal.
24 in. Son’s height
=
36 in.
70.5 in.
Substitute.
47 in.= Son’s height
Multiply each side by 70.5 and simplify.
3
2
89 SAS Similarity Theorem
90 Skew lines are lines that do not intersect and do not lie in the same plane.
88
4