MCQ Questions

Question No. 1

Find the ratio of a to b in:

Answer :

a) a/3 = b/2

b) 2a – 5b = 0

c) (a + b)/(a – b) = 7

Question No. 2

Solve:

Answer :

a) Construct an equilateral triangle with sides of 9 cm. What is the size of the angles of the triangle? Give a reason for the values that you have measured.

b) Construct an equilateral triangle with sides of 6 cm.

Question No. 3

Given xy = pq, form a proportion in which:

Answer :

a) x is one of the extremes

b) x is one of the means

c) p is the first term

Question No. 4

Find the value of x and y in these proportions.

Answer :

a) 9/x = 3/5

b) 3 : 5 = x : 4

c) 2/x = y/8 = 1/4

Question No. 5

Draw a square with sides 2 cm.

Answer :

Question No. 6

Draw a rectangle with length 3 cm and breadth 2 cm.

Answer :

Question No. 7

State the values of all four angles of the two quadrilaterals.

Answer :

Question No. 8

Use the two triangles to complete the statements.

Answer :

a) ∠ABC corresponds to ______

b) ∠BCA corresponds to ______

c) ∠CAB corresponds to ______

Question No. 9

ΔXYZ is similar to ΔKLM. Name all the corresponding sides.

Answer :

INNSSSSSSEEERRRRTTT IMAAAAGGEEEEE

Question No. 10

Are the following pairs of triangles similar? If they are similar, write the vertices in the correct order.

Answer :

a)

b)

c)

d)

Question No. 11

Given that ΔPQR is similar to ΔABC, complete the extended proportion AB/□ = BC/□ = CA/□ .

Answer :

INNSSSSSSEEERRRRTTT IMAAAAGGEEEEE

Question No. 12

Use ΔABZ in which Â = XŶZ to answer the questions that follow.

Answer :

a) Name two triangles in the diagram that are similar.

b) Complete the proportion XY/□ = ZY/□ = XZ/□ .

c) Given that XY = 4, BA = 10 and ZY = 2, find ZA.

Question No. 13

Given that a triangle has two angles equal to 35° and 20°, draw the triangle.

Answer :

a) Draw another triangle similar to the triangle in Question 1(a).

b) Draw a third triangle similar to the triangles in Question 1(a) and (b).

c) How many triangles can you draw that are similar to the first triangle?

Question No. 14

Giving reasons, state which of the following shapes are similar:

Answer :

a) any two isosceles triangles

b) any two equilateral triangles

c) any two squares

d) any two rectangles

e) any two rhombuses

f) any two trapeziums

g) any two regular polygons

h) any two regular polygons with the same number of sides

Question No. 15

Consider several examples of similar triangles. What can you conclude about the ratio of their perimeters?

Answer :

Question No. 16

Which of these triangles are not similar to triangle e)?

Answer :

Question No. 17

Find the scale factor for the sides of these pairs of similar triangles.

Answer :

a)

b)

c)

Question No. 18

Give reasons why each of these pairs of triangles are similar.

Answer :

a)

b)

c)

Question No. 19

In the right-angled triangle ABC, BD is perpendicular to AC.

Answer :

a) Find three pairs of triangles that are similar, stating reasons for your answer.

b) Write the corresponding ratios for each set of similar triangles.

Question No. 20

ABC is an isosceles triangle in which AB = AC and BD bisects ÂBC. Given that BÂC = 36°:

Answer :

a) Find two similar triangles in the figure.

b) Give reasons why the triangles in (a) are similar.

Question No. 21

In the figure, ABCD is a parallelogram. State reasons why ΔFDE and ΔBCE are similar.

Answer :

Question No. 22

The following diagram shows two similar triangles.

Answer :

a) What is the length of side GE?

b) What is the scale factor from ΔEFG to ΔEBD?

Question No. 23

The following diagram shows two similar rectangles.

Answer :

a) What is the scale factor from rectangle EFGH to rectangle ABCD?

b) What is the length of side CD?

Question No. 24

The following diagram shows three similar triangles.

Answer :

a) What is the length of side EG?

b) What is the scale factor of ΔHIJ to ΔEFG?

c) What is the perimeter ratio of triangle ΔEFG to ΔABC?

d) What is the length of side AB?

Question No. 25

Determine if the triangles below are similar, and explain your reasons. Find the lengths of the missing sides. All measures are in centimetres.

Answer :

a)

b)

c)

d)

e)

f)

Question No. 26

Given that ΔABC ||| ΔPQR:

Answer :

a) Calculate the ratio PR ⁄ AC.

b) Calculate x.

c) Calculate y.

Question No. 27

Find the value of x in each figure.

Answer :

a)

b)

c)

Question No. 28

Use graph or grid paper to find the image of A(7; 3), B(9; 3) and C(7; 8), taking the centre of enlargement at (0; 0) and a scale factor of ½.

Answer :

Question No. 29

Use graph or grid paper to find the images of the objects below, using the given centres of enlargement or reduction and scale factors.

Answer :

a) Object: A(2; 4), B(4; 2), C(5; 5); Centre: (0; 0); Scale factor: +3

b) Object: A(2; 4), B(4; 2), C(5; 5); Centre: (0; 0); Scale factor: −2

c) Object: A(2; 4), B(4; 2), C(5; 5); Centre: (0; 0); Scale factor: −½

d) Object: A(1; 2), B(1; 4), C(2; 4); Centre: (0; 0); Scale factor: +2

e) Object: A(2; 1), B(4; 1), C(4; 4), D(2; 4); Centre: (−2; −3); Scale factor: +4

f) Object: A(7; 6), B(11; 8), C(9; 10); Centre: (−3; −4); Scale factor: +½

g) Object: L(6; 4), M(10; 4), N(10; 8), P(6; 8); Centre: (4; 6); Scale factor: +3⁄2

Question No. 30

ΔPQR and ΔP′Q′R′ are object and image, respectively. In each case, plot the object and the image on the same set of axes and describe the enlargement or reduction fully.

Answer :

a) P(1; 0), Q(5; 1), R(1; 3) and P′(10; 9), Q′(2; 7), R′(10; 3)

b) P(2; 5), Q(9; 3), R(5; 9) and P′(13⁄2; 7), Q′(10; 6), R′(8; 9)

c) P(1; 2), Q(13; 2), R(1; 10) and P′(6; 6), Q′(12; 6), R′(6; 10)

Question No. 31

Find the ratio of the area of these pairs of similar triangles.

Answer :

a)

b)

Question No. 32

The ratio of the areas of two circles is 16 : 9. If the diameter of the larger circle is 8 cm, what is the area of the smaller circle?

Answer :

Question No. 33

Two cylinders, A and B, are similar. The base area of A is half the base area of B. If the base area of B is 100 cm², what is the base area of A?

Answer :

Question No. 34

X and Y are two similar cylinders. The radius of the base of X is half the radius of the base of Y, and the height of X is half the height of Y. What is the ratio of their volumes?

Answer :

Question No. 35

The sides of two squares measure 14 cm and 8 cm, respectively. Write in the simplest form:

Answer :

a) the ratio of the lengths of their sides

b) the ratio of their areas

Question No. 36

The plan of a house is drawn to scale, with 2 cm on the plan representing 1 m on land.

Answer :

a) A wall on the plan measures 6 cm. Find its actual length.

b) Determine the actual length represented on the plan by 60 cm.

c) A rectangular room on the plan measures 14 cm by 8 cm. Find the actual area of the room.

Question No. 37

Two circles are such that one has a radius of 8 cm and the other has a diameter of 24 cm. Write in the simplest form:

Answer :

a) the ratio of the radii

b) the ratio of the areas of the circles.

Question No. 38

Two similar jars have heights of 16 cm and 12 cm, respectively. Given that the smaller jar holds 0.81 litres when full, find the capacity of the larger jar when full.

Answer :

Question No. 39

Two rubber balls have diameters of 3 cm and 5 cm, respectively. Find in its simplest form:

Answer :

a) the ratio of their volumes

b) the ratio of their surface areas.

Question No. 40

A pole with height 1 m casts a shadow with length 3 m. At the same time, what is the length of the shadow of a similar pole with height 3 m?

Answer :

Question No. 41

A boy who is 1.5 m tall, stands 2 m from a street light and casts a shadow of length 2 m. What is the height above the ground of the street light?

Answer :

Question No. 42

A ladder rests with one end on the ground and the other end on a vertical wall that is 4.5 m high. A vertical pole with length 1.5 m is placed under the ladder at a distance of 2 m from the wall. Find the distance of the pole from the foot of the ladder.

Answer :

Question No. 43

A scale model of the school auditorium is made in the form of a cuboid, using a scale of 1 : 120. The size of the auditorium is 60 m by 42 m and it is 10.8 m high. Calculate:

Answer :

a) the length, breadth and height of the model

b) the area of the floor of the model

c) the volume of the model

d) the ratio volume of model ⁄ volume of auditorium .

Question No. 44

If the two triangles are similar, find the tower’s height from the given measurements alongside.

Answer :

Question No. 45

Consider the triangles in the figure below:

Answer :

a) Are the two triangles similar?

b) What is the length of QT?

c) If PT is 15 cm, what is the length of RT?

Question No. 46

Adaoma is 1.3 m tall. She stands 7 m in front of a tree and casts a shadow 1.8 m long. How tall is the tree?

Answer :

Question No. 47

Ifetundun casts a shadow of 1.2 m and she is 1.8 m tall. A building casts a shadow of 10 m at the same time that Ifetundun measured her shadow. Draw a diagram of this situation, and then calculate the building’s height.

Answer :

Question No. 48

Thales of Miletus (625 to 547 BC) was a Greek philosopher who travelled to Egypt. While there, the king of Egypt asked Thales to find out the height of a pyramid. He waited for the time of day when the shadow of his stick was as long as the stick was tall. He then measured the length of the shadow of the pyramid, which was of course, equal to its height. ΔABC is formed by the height of the pyramid, half the length of the pyramid and its shadow. ΔDEC is formed by Thale’s staff and the shadow cast

Answer :

a) the base of the pyramid is 230 m

b) the length of its shadow, FC, is 95 m

c) the length of Thales’ staff is 2 m

d) the length of its shadow is 3 m

Question No. 49

ΔIJK and ΔTUV are similar. The length of the sides of ΔIJK are 40, 50, and 24 units. If the length of the longest side of ΔTUV is 275 units, what is the perimeter of ΔTUV?

Answer :

Question No. 50

Iyawa wants to measure the height of a nearby flagpole using a mirror as shown in the diagram. The mirror is 6 m away from the flagpole and 2 m away from Iyawa. The height to her eyes is 1.57 m from which she can clearly see the top of the flagpole. How tall is the flagpole in centimetres?

Answer :

Question No. 51

Ndudioso wants to cross a river. To determine the width of the river, he locates a tree at Point A across the river. He marks the spot and then walks 28 m to Point C. He marks Point C and walks an additional 10 m before turning perpendicular to the river and walking until Point C lines up with Point A. This distance is 14 m. What is the width of the river in metres?

Answer :

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