Test 6 - Pearson

Form 3 Mathematics Test
Test 6: Properties of triangles
Total: 50 marks
Name: ________________________________________ Date: __________________________
Section A
Write down the correct letter for each of the following questions.
1. A line joining the midpoints of two sides of a triangle
A is equal to the third side
B is parallel to the third side
C divides the area of the triangle in two equal halves
D divides the area of the triangle in the ratio 1:3.
2. A line through the midpoint of one side of a triangle parallel to a
second side
A
B
C
D
is longer than the second side of the triangle
halves the second side of the triangle
equals half of the second side of the triangle
halves the third side of the triangle.
3. Two congruent triangles
A
B
C
D
have equal areas
have the same shape
map perfectly onto one another
look the same but their sizes differ.
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4. Which one of the following is not a condition for congruency of
two triangles
A
B
C
D
SSS
AAA
SAS
SAA
5. Two similar triangles
A
B
C
D
map perfectly onto one another
have equal areas
have all sides equal
have the same shape but differ in size.
6. Which one of the following is a condition for similarity of two triangles
A
B
C
D
two angles of one triangle equal to two angles of the other triangle
one angle and two sides of one triangle are equal to one angle and
two sides of the other triangle
three sides of one triangle are equal to three sides of the other
triangle
the triangles map perfectly onto one another.
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2/7
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Section B
7. In triangle PQR, M and N are the midpoints of PQ and PR respectively.
MN = 4.6 cm, P = 64° and MNP = 52°. Write down, with reasons:
P
64°
M
52°
N
Q
R
a) the size of PMN (2)
b) the size of PRQ (2)
c) the length of QR (2)
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3/7
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8. In triangle ABC, AR = RB, RS // BC, ABC = 70°, ASR = 40° and
RS = 3.8 cm. Write down, with reasons:
A
R
40°
S
B
70°
C
a) the size of ARS (2)
b) the size of BAC (2)
c) the length of BC (2)
d) the length of AC (2)
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4/7
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9. In triangle MNO, T and S are the midpoints of MO and NO respectively,
MN NO, M = 58° and MN = 2.8 cm. Write down, with reasons:
M
58° T
N
S
O
a) the size of MNO (2)
b) the size of MON (2)
c) the size of TSO (2)
d) the length of ST (2)
e) The ratio OT:OM in its simplest form (2)
10. In triangle DEF, DF = 6.4 cm, FE = 8.2 cm, D = 88° and F = 42°. In
triangle MRS, MS = 3.2 cm, S = 42°, and R = 50°.
D
88°
6.4 cm
M
E
F
42°
8.2 cm
3.2 cm
S
42°
50°
R
a) Calculate, with reasons, the size of E. (2)
b) Give reasons why ∆DEF /// ∆MRS. (2)
c) Write down the ratio MS:DF in its simplest form. (2)
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d) Calculate the length of RS. (2)
e) Write down the ratio DE:MR in its simplest form. (2)
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11. In triangles PQR and STM, PQ = ST = 4.7 cm, P = S and PR = SM.
In triangle STM, MT = 8 cm, M = 32° and T = 82°.
P
4.7 cm
x
Q
S
x
R
M
32°
8 cm
82°
T
a) Prove that ∆PQR ≡ ∆STM. (2)
Write down, with reasons:
b) the size of S (2)
c) the size of Q (2)
d) the length of ST (2)
e) the length of QR (2)
6/7
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Total: 50
7/7
Maths Test 6
© Pearson Botswana. Permission is given to photocopy these pages for school use.