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Question (1)

QN0030858

A student constructs the perpendicular bisector of a line segment PQ. Which statement is always true about any point on the perpendicular bisector?

(A) It is closer to P than to Q.
(B) It is equidistant from P and Q.
(C) It lies on PQ.
(D) It forms a 60° angle with PQ.

Correct Answer: B

Explanation:

Every point on the perpendicular bisector is at equal distances from the endpoints of the line segment.

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Question (2)

QN0030859

A line segment AB is 18 cm long. A point lies on its perpendicular bisector and is 15 cm from A. What is its distance from B?

(A) 9 cm
(B) 12 cm
(C) 15 cm
(D) 18 cm

Correct Answer: C

Explanation:

Points on the perpendicular bisector are equidistant from A and B.

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Question (3)

QN0030860

A student constructs a 60° angle and then bisects it. If the resulting angle is again bisected, what is the measure of the final angle?

(A) 10°
(B) 15°
(C) 20°
(D) 30°

Correct Answer: B

Explanation:

60° → 30° → 15°.

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Question (4)

QN0030861

Which construction is most useful for drawing a line through a point parallel to a given line using only a ruler and compass?

(A) Constructing equal corresponding angles
(B) Constructing a circle
(C) Constructing a square
(D) Constructing a rectangle

Correct Answer: A

Explanation:

Equal corresponding angles ensure that the two lines are parallel.

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Question (5)

QN0030862

A student copies an angle using only a ruler and compass. Which property ensures that the copied angle is equal to the original?

(A) Equality of corresponding sides in congruent triangles
(B) Equality of perimeters
(C) Equality of areas
(D) Equality of diagonals

Correct Answer: A

Explanation:

The copied construction is based on congruent triangles.

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Question (6)

QN0030863

A rectangular floor measures 8 × 11 unit squares. The minimum number of 2 × 1 tiles needed to cover it completely is

(A) 40
(B) 42
(C) 44
(D) It cannot be tiled completely.

Correct Answer: C

Explanation:

Total unit squares = 8 × 11 = 88. Tiles required = 88 ÷ 2 = 44.

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Question (7)

QN0030864

A 9 × 6 rectangular board has two opposite corner unit squares removed. Why is complete tiling with 2 × 1 tiles impossible?

(A) The remaining number of squares is odd.
(B) The removed corner squares are of the same colour in black-and-white colouring.
(C) The board becomes triangular.
(D) The tiles become too small.

Correct Answer: B

Explanation:

Removing two opposite corners removes two squares of the same colour, leaving unequal numbers of black and white squares.

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Question (8)

QN0030865

Which of the following regular polygons alone cannot tile the entire plane without gaps?

(A) Square
(B) Equilateral triangle
(C) Regular pentagon
(D) Regular hexagon

Correct Answer: C

Explanation:

Regular pentagons cannot tessellate the plane by themselves.

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Question (9)

QN0030866

A region has 24 black squares and 24 white squares after black-and-white colouring. Which conclusion is correct?

(A) The region is definitely tileable.
(B) The region is definitely not tileable.
(C) Equal numbers of black and white squares are necessary but may not be sufficient for tiling.
(D) The region can be tiled only with square tiles.

Correct Answer: C

Explanation:

Equal numbers of black and white squares are necessary, but they do not guarantee a tiling.

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Question (10)

QN0030867

A student wants to construct a regular hexagon using only a ruler and compass. Which construction should be completed first?

(A) Construct a 90° angle.
(B) Construct an equilateral triangle.
(C) Construct a 45° angle.
(D) Construct a rectangle.

Correct Answer: B

Explanation:

A regular hexagon is constructed using the 60° angle obtained from an equilateral triangle.

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Question (1)

A student constructs the perpendicular bisector of a line segment PQ. Which statement is always true about any point on the perpendicular bisector?

Explanation:

Link:

Question (2)

A line segment AB is 18 cm long. A point lies on its perpendicular bisector and is 15 cm from A. What is its distance from B?

Explanation:

Link:

Question (3)

A student constructs a 60° angle and then bisects it. If the resulting angle is again bisected, what is the measure of the final angle?

Explanation:

Link:

Question (4)

Which construction is most useful for drawing a line through a point parallel to a given line using only a ruler and compass?

Explanation:

Link:

Question (5)

A student copies an angle using only a ruler and compass. Which property ensures that the copied angle is equal to the original?

Explanation:

Link:

Question (6)

A rectangular floor measures 8 × 11 unit squares. The minimum number of 2 × 1 tiles needed to cover it completely is

Explanation:

Link:

Question (7)

A 9 × 6 rectangular board has two opposite corner unit squares removed. Why is complete tiling with 2 × 1 tiles impossible?

Explanation:

Link:

Question (8)

Which of the following regular polygons alone cannot tile the entire plane without gaps?

Explanation:

Link:

Question (9)

A region has 24 black squares and 24 white squares after black-and-white colouring. Which conclusion is correct?

Explanation:

Link:

Question (10)

A student wants to construct a regular hexagon using only a ruler and compass. Which construction should be completed first?

Explanation:

Link:

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