Download A) Two triangles having corresponding sides congruent

1
2
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.
Which of the four pairs of triangles below consists of two triangles that are definitely congruent?
A)
C)
4 cm
98°
3 cm
3 cm
40°
5 cm
4 cm
45°
5 cm
45°
98°
40°
5 cm
B)
D)
45°
105°
30°
10 cm
10 cm
105°
5 cm
3
The following diagram shows lines AB, CD, EF and GH
G
F
In addition:
AB // CD
A
K
B
?
m  DLH = 75
(2x)
m  KJL = (3x)
m  LKJ = (2x)
C
J
(3x)
L
D
75
E
H
A
B
?
3x
4
In the figure, quadrilaterals ABCP and ABPD are parallelograms.
What is the measure of angle BAP?
2x
65
D
5
P
C
Louise wants to buy the piece of land corresponding to
triangle BAE shown in the rectangle.
What is the area of this piece of land?
C
6
The mast of a sail is secured with two guy wires as shown in the adjacent
figure. The angle formed at the point where the 2 guy wires are attached
st
to the top of the mast is 90. The 1 guy wire is attached to the deck 26 m
nd
from the foot of the mast. The 2 guy wire is attached 19 m from the foot
st
of the mast at the opposite end of the deck. During a storm, the 1 guy
wire broke.
What length of cable is needed to replace it?
2nd guy wire
1st guy wire
mast
B
26 m
19 m
D
B
F
7
D
In the figure on the right,



Lines AB and CD are parallel.
Lines AB, ED and FG intersect at point I.
Lines CD and FG intersect at point H.
E
I
A
Which of the following statements allows you to state that angle FIB is
congruent to angle GHC?
H
C
A)
Vertically opposite angles are congruent.
B)
Corresponding angles formed by two parallel lines and a transversal are
congruent.
C)
Alternate interior angles formed by two parallel lines and a transversal are
congruent.
D)
Alternate exterior angles formed by two parallel lines and a transversal are
congruent.
G
A
A
?
8
In the following figure:
R
B
Lines RC and DQ are parallel.
C
120
Lines BD and CP intersect at point A.
m  CBD = 120
D
Q
40
E
m  QEP = 40
The following is part of a procedure used to determine the
measure of angle BAC.
P
Complete steps 1 and 2 of this procedure.
Step 1
m  ABC + m  CBD = 180
because
m  ABC + 120 = 180
m  ABC = 60
Step 2
m  BCA = m  QEP = 40
because
Step 3
m  ABC + m  BCA + m  BAC = 180
because the sum of the measures of the interior
angles of a triangle is 180.
60 + 40 + m  BAC = 180
m  BAC = 80
B
9
Isaac is building a house for his dog, Newton. His design is
measured in decimetres. Triangle ABC is isosceles and angles
APM, BMA and BQM each measures 90°.
P
What is the measure of each roof support, represented by
segments
9 dm
Q
PM and QM ?
A
M
24 dm
C
A
10
In the adjacent circle with centre O,


CD is perpendicular to AB at point D
m BD = 4 cm

m OC = 13.5 cm
O
4 cm
13.5 cm
C
D
B
A
B
What is the area of triangle ABC?
11
C
In the adjacent figure, C is the midpoint of segments AE and BD.
Prove that triangles ABC and CDE are congruent. Justify your statements.
E
D
Statements
12
Justifications
Triangle ABC is inscribed in semicircle with centre O.
A
BC is a diameter and AD  BC .
m BA = 17 cm
m BD = 15 cm
What is the area of the shaded region?
B
O
D
C
A
B
13
14
3m
Cable
In a circus, a tightrope walker must
walk along two cables. The ends of
Cable
C
these cables are attached to anchor
Ground
points. As indicated in the diagram, the
15 m
horizontal distance between anchor
points A and B is 15 m. Anchor point A is located 3 m above the ground, and anchor point B is located 2
m above the ground. Anchor point C, to which both cables are attached, is located at ground level. Line
segments AC and BC represent the cables. Anchor point C is positioned so as to minimize the total
combined length of the two cables.
A
What is the total combined length of the two cables?
2m
Fred must make a sail in the shape of a right triangle for his boat
by sewing together four different-coloured triangular pieces of
canvas.
Fred must use the measurements indicated on the following
6.4 m
pattern.
The pieces of canvas will be sewn together along 3 seams, which
are represented on the pattern by segments AB, BC and CD. Fred
wants the total length of seams AB and BC to be as short as
possible.
C
0.8 m
What is the minimum total length of seams AB and BC, in metres?
B
5.4 m
15
Triangle MNO has the following characteristics:
• mMNO = 35
• mNMO = 45
• m NO = 10 m
Which one of the triangles below must be congruent to triangle MNO?
A)
Q
P
C)
35
45
Q
P
35
10 m
100
R
R
B)
Q
P
45
D)
10 m
P
100
R
100
Q
35
45
10 m
R
D
16
Equilateral triangle ABC is shown on the right.
A
Line segments AD and BE have been drawn.
Point D is a point on segment BC.
E
Point E is a point on segment CA
In addition, segments BD and CE are congruent.
The following is part of a procedure used to show that
segments AD and BE are congruent. Complete steps 4 and
5 of this procedure.
B
D
C
In triangles ABC and BCE:
Step 1
 ABC   BCA
because in an equilateral triangle, each of the
interior angles measures 60.
Step 2
AB  BC
because the 3 sides of an equilateral triangle are
equal in length.
Step 3
BD  CE
by hypothesis
Step 4
 ABD   BCE
because ...
Step 5
AD  BE
because ...