Chapter 7:Geometrical Constructions

Paper 1This test paper contains 20 questions. Answer ALL the questions.The diagrams accompanying the questions are not drawn to scale unless mentioned.You are allowed to use a scientific calculator that cannot be programmed.

1 Which of the following triangles cannot be drawn?

4 cm 7 cm 10 cm 6 cm 8 cm 2 cm

8 cm 15 cm7 cm

I II III IV

A I only C I and IV onlyB I and II only D I and III only

2 The angle of 120° can be constructed by usingI a pair of compassesII a rulerIII a protractorA I only C I, II and IIIB I and II only D None of the above

3 Diagram 1 shows the steps in the construction of a triangle.

P Q R S

DIAGRAM 1

Which of the following statements is true?A It is the construction of an isosceles triangle.B The correct order of the steps is S, Q, R and P.C It is the construction of an equilateral triangle.D It is the construction of a scalene triangle.

1

6 cm

4 Diagram 2 shows an incomplete construction.

DIAGRAM 2

Which of the statements below is not true?A It is a construction of a regular hexagon.B It is a construction of an angle of 60°.C It is a construction of an angle of 120°.D It is a construction of a square.

5 Diagram 3 shows the construction of an angle.

E D C

A O B

DIAGRAM 3

Which of the following angles is equal to 90°?A AOD C COBB EOB D DOC

2

6 Which of the following figures shows a perpendicular bisector of line segment MN?A C

M N M N

B D

M N M N

7 Diagram 4 shows the construction of an angle.

H H

P M Q Q

P M

K K

I II III

DIAGRAM 4

Which of the following statements is not true about the construction?A The correct order of the steps are III, I and II.B PM = MQC PH = HQD PKQ = 90°

3

P

8 Which of the following shows the correct way of constructing parallel lines?

A C

B D

9 Diagram 5 shows a construction.

P O Q R

DIAGRAM 5

The diagram shows the construction ofA an angle of 60°B a perpendicular bisector of PRC a perpendicular line through OD an equilateral triangle

4

10 Diagram 6 shows the construction of a perpendicular bisector.

R

M

P Q

DIAGRAM 6

In the diagram, _________ is a perpendicular bisector of __________________.A PQ, RMB PR, QMC RQ, PMD PM, QR

11 Diagram 7 shows the construction of an angle.

C

B

A O

DIAGRAM 7

From the construction, if AOC is of AOB, find the angle of AOC.

A 40° C 80°B 60° D 120°

12 Diagram 8 shows the construction of a parallelogram.

50°

DIAGRAM 8

Which of the following instruments are needed to construct the parallelogram?I RulerII Set squareIII A pair of compassesIV ProtractorA II and III C I, III and IVB I, II and III D All of the above

5

13 Diagram 9 shows the construction of an angle.

C

O B

A

DIAGRAM 9

Which of the following statements is false?A AOC = 60°

B BOA = AOC

C BOA = 15°D BO is the bisector of AOC

14 Diagram 10 shows the construction of a triangle.

6 cm

45°

5 cm

DIAGRAM 10

To construct the triangle, you may need a I a rulerII a set squareIII a pair of compassesIV a protractorA I only C IV onlyB III only D I and III only

6

15 In Diagram 11, P and Q are the centres of the two identical circles.

P Q

R

DIAGRAM 11

Which of the following statements is false?A PRQS is a rhombusB SPR = 120°C PQR = 60°D PQ = SR

16 Diagram 12 shows the construction of an angle.

B C

A O

DIAGRAM 12

BOA isA 30° C 60°B 45° D 120°

7

S

B

17 Diagram 13 shows the steps of a construction.

6 cm6 cm

P 5 cm Q P 5 cm Q

I III

6 cm

P 5 cm Q P 5 cm Q

II IV

DIAGRAM 13

Which of the following statements is false?A It shows a construction of an isosceles triangle.B The correct order of the steps is I, II, III and IV.C PQ is called a line segment.D Q is the centre to draw the arc in figure IV.

18 Diagram 14 shows angle POQ = 130°.

R

Q

O P

DIAGRAM 14

Find the value of ROP.A 60° C 70°B 65° D 120°

8

19 Diagram 15 shows a certain construction.

•

P Q

DIAGRAM 15

It is the construction ofA a perpendicular bisectorB a line perpendicular to PQ and passing through the point RC a parallelogramD an angle bisector

20 Diagram 16 shows four triangles.

60° 5 cm 8 cm

50° 8 cm

7 cmI III

6 cm 120° 7 cm 5 cm

10 cmII IV

DIAGRAM 16

Which of the triangles can be constructed by using a ruler and a pair of compasses? A I and II onlyB I, II and III onlyC I, II and IV onlyD All of the above

9

R

Paper 2This test paper contains 10 questions. Answer ALL the questions.The diagrams accompanying the questions are not drawn to scale unless mentioned.You are not allowed to use a calculator.

1 Use a pair of compasses and a ruler to construct a line perpendicular to PQ and passing through the fixed point R.

• R

P Q

2 Diagram 1 is a quadrilateral.

9 cm6 cm

60°

12 cm

DIAGRAM 1

Construct the figure using a pair of compasses and a ruler only.

3 Diagram 2 is a quadrilateral.

5 cm 8 cm

45° 60°

13 cm

DIAGRAM 2

Construct the following figure without using a protractor.

10

4 In Diagram 3, PQ and QR are straight lines.

R

DIAGRAM 3

Construct the bisector of PQR.

5 In Diagram 4, PQRS is a quadrilateral.

P Q

120° 80°

8 cm

S R

DIAGRAM 4

Construct the diagram.

6 In Diagram 5, PQ is a straight line.

P Q

DIAGRAM 5

Construct angle PQR which is 150°.

7 In Diagram 6, PQR is a triangle.

8 cmR Q

7 cm 7 cm

P

DIAGRAM 6

11

Q P

10 cm

Construct the triangle and measure the angle RQP.

12

2 8 Diagram 7 shows a right-angled triangle.

5 cm

7 cm

DIAGRAM 7

Construct the triangle below without using a protractor.

9 In Diagram 8, ABC is a triangle.

A 7.5 cm B

60°

4.5 cm

C

DIAGRAM 8

Construct ABC. Then construct a perpendicular bisector of the line AB.

10 In Diagram 9, ABCD is a parallelogram.

A B

5.8 cm

D C6.7 cm

DIAGRAM 9

Construct the parallelogram and then construct the midpoint of AC. Measure the distance from the midpoint to D.

13