Regular revision with Class 7 Maths MCQ with Answers and Ganita Prakash Class 7 Maths Part 2 Chapter 6 Constructions and Tilings MCQ improves accuracy in objective exams.
MCQ on Constructions and Tilings Class 7
Constructions and Tilings MCQ Class 7
Class 7 Maths Constructions and Tilings MCQ
Question 1.
If we bisect a line segment AB of 9 cm, then what will be the length of each part?
(a) 5 cm
(b) 4 cm
(c) 4.5 cm
(d) 3 cm
Solution:
(c) 4.5 cm
When we bisect a line segment, the length of each part is half of the length of given line segment.
Given, length of the line segment AB = 9 cm After bisecting AB,
Length of each part = (Length of the line segment AB) ÷ 2 = 9 cm ÷ 2 = 4.5 cm.
Question 2.
Two lines are said to be perpendicular if angle between them is:
(a) 45°
(b) 90°
(c) 60°
(d) 30°
Solution:
(b) 90°
We know, two lines are said to be perpendicular if angle between them is 90°.
Question 3.
To construct the perpendicular bisector of a line segment PQ, the compass opening must be:
(a) smaller than half of PQ
(b) more than half of PQ
(c) equal to the length of PQ
(d) equal to half of PQ
Solution:
(b) more than half of PQ
To construct the perpendicular bisector of a line segment PQ, the compass opening must be more than half of PQuestion
Question 4.
If we bisect an angle of a rectangle, we get two angles each of:
(a) 45°
(b) 30°
(c) 60°
(d) 15°
Solution:
(a) 45°
We know that the measure of each interior angle of a rectangle is 90°.
Therefore, if we bisect an angle of a rectangle, we get two angles each of 45°.
Question 5.
What angle would you get if you bisect an exterior angle of an equilateral triangle?
(a) 90°
(b) 60°
(c) 45°
(d) 30°
Solution:
(b) 60°
We know that at each vertex of an equilateral triangle, the measure of exterior angle is 120°.
Therefore, if we bisect an exterior angle of an equilateral triangle, we get two angles measuring 60° each.
Question 6.
If YA = AB and AC = BC, then measure of ∠XYC equals:
(a) 60°
(b) 45°
(c) 30°
(d) None of these
Solution:
(c) 30°
Here, the arc from Y cuts YZ and YX at points A and B respectively and YD bisects ∠XYZ.
As arc radius is same, YA = YB.
∴ YA = YB = AB [Given, YA = AB]
Thus, ∆ABY is an equilateral triangle.
∴ ∠AYB = 60° ⇒ ∠XYC = 60° ÷ 2 = 30°
Question 7.
While constructing the perpendicular bisector of a line segment PQ, if the compass opening is exactly half of PQ, then drawn arcs from P and Q:
(a) do not intersect
(b) intersect at one point
(c) intersect at two points
(d) intersect at four points
Solution:
(b) intersect at one point
While constructing the perpendicular bisector of a line segment PQ, if the compass opening is exactly half of PQ, then drawn arcs from P and Q intersect at one point only.
Question 8.
Which of the following shapes can tile a plane on its own without leaving any gaps or overlaps?
(a) Circle
(b) Oval
(c) Square
(d) Regular pentagon
Solution:
(c) Square
A regular polygon can tile the plane only if its interior angle divides 360° exactly.
Circles and ovals leave gaps, and regular pentagons also fail to tessellate. Squares, however, fit together perfectly and cover the plane without gaps or overlaps.
Question 9.
A 5 × 5 square grid consists of 25 unit squares. Can it be completely covered using 2 × 1 dominoes?
(a) Yes, because 25 squares can be covered by dominoes in different ways.
(b) Yes, because dominoes can be placed both horizontally and vertically.
(c) No, because each domino covers 2 squares, and 25 is an odd number.
(d) None of the above
Solution:
(c) No, because each domino covers 2 squares, and 25 is an odd number.
Each 2 × 1 domino covers exactly 2 unit squares. To completely cover a grid, the total number of squares must be divisible by 2.
Here, the 5 × 5 grid has 25 unit squares. Since 25 is odd, it is not divisible by 2, so it is impossible to cover the entire grid with 2 × 1 dominoes.
Question 10.
Which of the following shapes does not tessellate (tile) a plane on its own?
(a) Equilateral triangle
(b) Square
(c) Hexagon
(d) Circle
Solution:
(d) Circle
Among the given shapes, only equilateral triangles, squares, and regular hexagons can tile the plane by themselves as their interior angle divides 360° exactly.
Question 11.
In a tangram set, which piece has all its sides equal in length?
(a) Square
(b) Parallelogram
(c) Small triangle
(d) Large triangle
Solution:
(a) Square
The tangram set consists of different shapes such as triangles, a square, and a parallelogram. A square has four sides of equal length.
A parallelogram has only opposite sides equal. The small triangles and the large triangles are right-angled isosceles triangles, which have only two sides equal, not all.
Question 12.
The tiling pattern used by bees in honeycombs is based on which of the following shapes?
(a) Squares
(b) Triangles
(c) Hexagons
(d) Pentagons
Solution:
(c) Hexagons
Bees construct honeycombs using hexagonal cells.
Constructions and Tilings Class 7 Fill in the Blanks
Question 1.
If two line segments cut each other at right angles, then they are _________ .
Solution: perpendicular
If two line segments cut each other at right angles, then they are perpendicular.
Question 2.
A straight angle can be bisected into _______ right angles.
Solution: two
We know that a straight angle measures 180°.
When a straight angle is bisected, it is divided into two equal angles, each measuring 90°.
Thus, a straight angle can be bisected into two right angles.
Question 3.
If ray OR bisects ∠POQ of measure 85°, the then they are measure of ∠POR is _______ .
Solution: 42.5°
Given, ∠POQ = 85°
And, ray OR bisects ∠POQ.
Therefore, ∠POR = ∠POQ ÷ 2 = 85° ÷ 2 = 42.5°