Download INTRO TO MATH 426 SOME REVIEW QUESTIONS FOR JANUARY

INTRO TO MATH 426
SOME REVIEW QUESTIONS FOR JANUARY EXAM
PART 1 – MULTIPLE CHOICE – Pick the correct answer.
1
2
3
Which of the following statements is true?
A)
Two similar squares are always isometric.
B)
Two equivalent squares are always isometric.
C)
Two similar triangles are always isometric.
D)
Two equivalent triangles are always isometric.
In which of the following cases are triangles ABC and DEF isometric?
A)
m B = 35
m E = 35
m AC = 6 cm
m DE = 6 cm
m BC = 5 cm
m EF = 5 cm
B)
m C = 40
m D = 40
m AB = 6 cm
m DE = 6 cm
m BC = 5 cm
m EF = 5 cm
C)
m A = 75
m D = 75
m B = 35
m E = 70
m BC = 5 cm
m EF = 5 cm
D)
m A = 70
m D = 70
m AB = 5 cm
m DE = 5 cm
m AC = 10 cm
m EF = 10 cm
The following are the equations of two perpendicular lines:
y = cx + d
y = ex + f
Which of the following statements is TRUE?
A)
c=e
C)
c=
1
e
B)
c = -e
D)
c=
-1
e
4
Given the triangles illustrated below.
B
D
H
E
A
F
I
G
C
Which of the following statements are TRUE?
1.
2.
3.
5
6
Triangle ABC is similar to triangle DFE.
Triangle ABC is equivalent to triangle HGI.
Triangles ABC and DFE are isometric.
A)
1 and 2 only
C)
2 and 3 only
B)
1 and 3 only
D)
1, 2 and 3
What is the slope of the line
x
y
  1?
3
7
A)
-
7
3
C)
3
7
B)
-
3
7
D)
7
3
The equations of two parallel lines are as follows:
2x  5y  10 = 0
2x  5y + 4 = 0
Rounded to the nearest tenth, what is the distance between these two lines?
A)
2.5 units
C)
2.7 units
B)
2.6 units
D)
2.8 units
7
In the figure below, diagonal AC bisects angles A and C.
B
C
A
D
Which property can be used to prove that triangles ABC and ADC are isometric?
8
A)
If the corresponding sides of two triangles are isometric, then the triangles are
isometric.
B)
If two angles and the contained side of one triangle and the corresponding two angles
and contained side of another triangle are isometric, then the triangles are isometric.
C)
If two sides and the contained angle of one triangle and the corresponding two sides
and contained angle of another triangle are isometric, then the triangles are isometric.
D)
If two angles of one triangle and the two corresponding angles of another triangle are
isometric, the triangles are isometric.
The following are the equations of two lines:
y  cx 
 where c  1
y  - cx 
Which of the following statements is true?
A)
These two lines are perpendicular.
B)
These two lines are parallel and distinct.
C)
These two lines are parallel and coincident.
D)
These two lines intersect, but are not perpendicular.
9
Given the triangle ABC below:
B
14
65
45
C
A
Which of the following triangles is necessarily isometric to triangle ABC?
Note that the figures are not necessarily drawn to scale.
A)
C)
I
J
70
14
45
K
L
65
70
H
14
B)
G
D)
F
N
14
D
45
45
14
E
M
70
65
O
PART 2 – DEVELOPMENT QUESTIONS – Show all your steps.
10
Mr. Greensleeves wants to plant an exotic tree approximately 1 metre high on the north side of
his house.
Knowing that this tree should receive maximum shade, he drew the following diagram :
Rounded to the nearest tenth of a metre, what should be the maximum distance d between the
tree and the house?
11
In the figure below, quadrilaterals ABCP and ABPD are parallelograms.
A
B
?
3x
2x
65
D
What is the measure of angle BAP?
P
C
12
In a Cartesian plane, the coordinates of the vertices of triangle ABC are A(1, 1), B(7, 1) and
C(9, 7). The median AM is also drawn.
y
C(9, 7)
M
A(1, 1)
B(7, 1)
x
What is the perimeter of triangle AMB, to the nearest tenth?
13
In the Cartesian plane on the right, sections
of a highway are represented by two parallel
lines.
y
The equation of the line representing the
southbound section is
(-21, 41)
y=
2
x + 30.
3
The line representing the northbound section
passes through the point (-21, 41).
What is the equation of the line representing the northbound section?
Give your answer in all 3 forms (just for practise!!!)
northbound
section
southbound
section
x
14
In the diagram on the right, triangle ABC
represents the mainsail of a sailboat.
A
2m
C
3m
4m
B
What is the height, AC, of the mainsail?
Give your answer in metres.
15
In the Cartesian plane on the right, points A, B
and C represent the location of three towns. A
hiking trail connects towns A and B.
The residents of town C want to build a new
trail represented by dotted line PC.
y
A (0, 30)
C (40, 17)
The new trail must be as short as possible.
P
B (12, 0)
What should be the coordinates of the point of intersection P?
Note that the diagram is not necessarily to scale.
x
16
In the Cartesian plane on the right, a dilatation
with centre C is applied to triangle ABC in
order to produce triangle PRC.
Y
B (65, 118)
R (80, 82)
A
(20, 58)
P
C (110, 10)
x
What are the coordinates of point P?
17
In trapezoid ABCD illustrated below, segment PQ is drawn parallel to the bases, making
trapezoid ABQP similar to trapezoid PQCD.
60 cm
A
70 cm
B
50 cm
Q
P
D
C
135 cm
What is the length of segment AP in cm?
MORE MULTIPLE CHOICE QUESTIONS
ON CONGRUENT TRIANGLES
1
There is one piece missing from the following geometric jigsaw puzzle.
4 cm
30
4.96 cm
8 cm
23.8
From the information given, which of the designs below can be used to make a piece congruent
to the missing one?
A)
C)
30
4 cm
8 cm
23.8
126.2
30
B)
D)
4 cm
126.2
4.96 cm
126.2
23.8
30
2
If the only information available is given on the diagrams below, which pair of triangles below
must be congruent?
The figures are not drawn to scale.
A)
Diagram 1
C)
Diagram 3
15 cm
10 cm
32
30
10 cm
7 cm
10 cm
30
22 cm
15 cm
B)
Diagram 2
D)
Diagram 4
15 cm
10 cm
32
30
10 cm
19 cm
60
10 cm
10 cm
98
50
15 cm
3
Which of the following statements is FALSE?
A)
Two triangles having corresponding sides congruent are necessarily congruent.
B)
Two triangles having three corresponding angles congruent are necessarily congruent.
C)
Two triangles having one congruent angle contained between two corresponding
congruent sides are necessarily congruent.
D)
Triangle ABC is congruent to triangle DEF and triangle DEF is congruent to triangle
MNP; therefore triangle ABC is necessarily congruent to triangle MNP.
4
A glass manufacturer has to replace the pieces of the following rectangular window.
1
2
Which one of the following statements does NOT explain the congruence of sections 1 and 2?
5
A)
Sections 1 and 2 have their 3 corresponding sides congruent.
B)
Sections 1 and 2 have their three corresponding angles congruent.
C)
Sections 1 and 2 have two corresponding sides and the included angle congruent.
D)
Sections 1 and 2 have two corresponding angles and the side between them
congruent.
In which of the following situations is there enough information to conclude that triangles ABC
and DEF are congruent?
A)
m B = 45
m E = 45
m AB = 12 cm
m EF = 12 cm
m AC = 6 cm
m DF = 6 cm
B)
m C = 60
m F = 60
m AC = 4 cm
m DF = 4 cm
m BC = 9 cm
m EF = 9 cm
C)
m A = 75
m D = 75
m B = 45
m E = 45
m AB = 8 cm
m DF = 8 cm
D)
m A = 75
m D = 75
m C = 60
m F = 60
m AB = 10 cm
m EF = 10 cm
6
Which of the following triangles is congruent to
the one illustrated at the right?
25 cm
46
113
49 cm
63 cm
21
A)
C)
46
113
25 cm
25 cm
113
49 cm
B)
D)
25 cm
42 cm
46
21
54 cm
49 cm
7
Given triangles ABC and DEF.
A
D
65
13.7 cm
12.6 cm
8 cm
80
B
80
8 cm
65
C
F
E
Which of the following reasons can be used to explain why triangles ABC and DEF are
congruent?
A)
If two angles of one triangle are congruent to two angles of another triangle, then the
triangles are congruent. (AA)
B)
If two sides and the contained angle of one triangle are congruent to two sides and the
contained angle of another triangle, then the triangles are congruent. (SAS)
C)
If two angles and the contained side of one triangle are congruent to two angles and
the contained side of another triangle, then the triangles are congruent. (ASA)
D)
If three sides of one triangle are congruent to three sides of another triangle, then the
triangles are congruent. (SSS)
8
In the figure below
AB  BC  FE  ED
A  BCF  CFE  D
B
C
A
D
F
E
Using this information, which two triangles can be proven congruent?
A)
BCF  EFC
C)
CFE  CDE
B)
BCF  BAF
D)
ABF  DEC
ANSWERS
PART 1:
1. B
2. C
3. D
4. D
5. A
6. B
7. B
8. D
PART 2:
12. p  16.8 units
11. 46o
10. 5.5 m
2
x  55
3
General form: 2 x  3 y  165  0
x
y
Symmetric form:

1
165
55
2
13. Functional form: y 
14. 8 m
15. P (10 , 5)
16. P (50 , 42)
17. m AP  28cm
MORE MULTIPLE CHOICE QUESTIONS :
1. B
2. D
3. B
4. B
5. B
6. C
7. C
8. A
9. A