Solved Questions on Construction
1. Which of the following is the correct arrangement of steps for constructing trapezium ABCD?
Steps for construction of trapezium ABCD are as follows:
1. From point A, draw a ray AR, making a 90° angle with AB. Mark off a segment AE of length 3.9 cm along this ray.
2. Connect vertices A and D and vertices B and C to form the trapezium ABCD.
3. From vertex B, use a compass with a radius of 4.7 cm to draw another arc.
4. From vertex A, use a compass with a radius of 5.4 cm to draw an arc.
5. Draw a line segment AB with a length of 7.2 cm.
6. The intersections of these arcs with line PQ are vertices D and C.
7. At vertex E, draw a line PQ parallel to the line segment AB.
a) 5 → 1 → 7 → 3 → 4 → 6 → 2
b) 5 → 1 → 7 → 4 → 3 → 6 → 2
c) 5 → 1 → 7 → 4 → 3 → 6 → 2
d) 5 → 1 → 7 → 4 → 3 → 6 → 2
Answer: b) 5 → 1 → 7 → 4 → 3 → 6 → 2
Explanation: Steps for construction of trapezium ABCD are as follows:
i. Draw a line segment AB with a length of 7.2 cm.
ii. From point A, draw a ray AR, making a 90° angle with AB. Mark off a segment AE of length 3.9 cm along this ray.
iii. At vertex E, draw a line PQ parallel to the line segment AB.
iv. From vertex A, use a compass with a radius of 5.4 cm to draw an arc.
v. From vertex B, use a compass with a radius of 4.7 cm to draw another arc.
vi. The intersections of these arcs with line PQ are vertices D and C.
vii. Connect vertices A and D and vertices B and C to form the trapezium ABCD.
2. Use a ruler and compass to construct a parallelogram with diagonals 8.5 cm and 10.5 cm in length that has an acute angle between them is 60°. Which of the following is the correct construction?
a) 
b) 
c) 
d) 
Answer: c) 
Explanation: Steps for construction of parallelogram ABCD are as follows:
i. Begin by drawing a line segment AC with a length of 8.5 cm.
ii. Identify the midpoint O of AC as diagonals of a parallelogram bisect each other. Draw perpendicular MN to get the vertex O.
iii. Draw an angle of 60° at vertex O.
iv. From point O, cut OB at 5.25 cm and from point O, cut OD at 5.25 cm.
v. Connect vertices A, B, C and D to complete the construction of the required parallelogram ABCD.
3. Which of the following is NOT correct for a quadrilateral KITE whose construction is shown below?
a) KITE is a rhombus in which ∠KIT is 135°.
b) KITE is a rhombus in which ∠KET is 135°.
c) KITE is a rhombus in which ∠IKE is 45°.
d) KITE is a rhombus in which ∠KIE is 45°.
Answer: d) KITE is a rhombus in which ∠KIE is 45°.
Explanation: KITE is a rhombus in which ∠KIE is half of 135° which is 67.5°.
4. Which of the following is correct for a quadrilateral BEAR with diagonal AB = 5 cm and ∠BAE = 45° whose construction is shown below?
a) BEAR is a rhombus in which AB is perpendicular to ER.
b) BEAR is a square in which AB is perpendicular to ER.
c) BEAR is a rhombus in which AB is not perpendicular to ER.
d) BEAR is a square in which AB is not perpendicular to ER.
Answer: b) BEAR is a square in which AB is perpendicular to ER.
Explanation: Diagonal AB is the bisector of ∠A. If ∠BAE = 45°, the ∠RAB = 45°.
∠BAE + ∠RAB = 45° + 45°
∴ ∠A = 90°
All sides are equal to 7.5. Both diagonal AB and ER are perpendicular to each other and equal to 5 cm.
Hence, BEAR is a square in which AB is perpendicular to ER.
5. Identify the incorrect statements for the following construction of quadrilateral DOVE.
A: Dove is a rectangle in which EV is perpendicular to QO.
B: Dove is a rectangle in which EV is perpendicular to DO.
C: Dove is a parallelogram in which EV is perpendicular to QO.
D: Dove is a parallelogram in which EV is perpendicular to DO.
a) A, B and D
b) A, C and D
c) B, C and D
d) B, C and A
Answer: c) B, C and
Explanation: Dove is a rectangle whose adjacent angles (∠D and ∠O) are 90° and whose opposite sides are equal.
Dove is a rectangle in which EV is perpendicular to QO.
Only statement A is correct. Statements B, C and D are incorrect statements.
