Chapter 7 - Geometrical Constructions
-
Upload
sarvesvari-raja-sagaran -
Category
Documents
-
view
65 -
download
2
Transcript of Chapter 7 - Geometrical Constructions
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