Explore numerous Class 7 Maths MCQ and Ganita Prakash Class 7 Maths Chapter 6 Constructions and Tilings MCQ Online Test with Answers provided with detailed solutions by looking below.
MCQ on Constructions and Tilings Class 7
Constructions and Tilings MCQ Class 7
Class 7 Maths Constructions and Tilings MCQ
Question 1.
In the construction of a perpendicular bisector of a line segment XY, if points P and Q are chosen such that PX=PY and QX = QY, what is the relationship between the line PQ and the segment XY?
(a) PQ is parallel to XY
(b) PQ is the perpendicular bisector of XY
(c) PQ intersects XY at a 45° angle
(d) PQ is half the length of XY
Solution:
(b) PQ is the perpendicular bisector of XY
Question 2.
To construct a 90° angle at a point O on a line l, which of the following is a valid method?
(a) Draw a circle around O
(b) Take equal distances OX and OY on the line, then construct the perpendicular bisector of XY
(c) Draw a 60° angle and bisect it
(d) Use a protractor to mark 90°
Solution:
(b) Take equal distances OX and OY on the line, then construct the perpendicular bisector of XY
Question 3.
Which of the following angles CANNOT be constructed using only a compass and straightedge (by angle bisection and 60°/90° construction)?
(a) 30°
(b) 22.5°
(c) 65.5°
(d) 75°
Solution:
(c) 65.5°
Question 4.
If a rectangular floor of 8m × 6m is to be tiled with square tiles of side 2 m, how many tiles are needed?
(a) 10
(b) 12
(c) 16
(d) 24
Solution:
(b) 12 (Total Area =48 m², Tile Area =4m². 20.
48 ÷ 4=12
Question 5.
When constructing a perpendicular bisector, is it necessary to have the same radius for the arcs above and below the line segment?
(a) Yes
(b) No
(c) Only for the top arcs
(d) Only for the bottom arcs
Solution:
(b) No (As long as the radii are consistent for the pairs of arcs, they can differ between the top and bottom pairs)
Question 6.
A regular tiling pattern can be formed using which of the following regular polygons?
(a) Regular pentagons
(b) Regular heptagons
(c) Regular hexagons
(d) Regular octagons
Solution:
(c) Regular hexagons (They can fill a plane without gaps)
Question 7.
To divide a line segment AB into four equal parts, how many times must you perform the perpendicular bisector construction?
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
(c) 3 (First bisect the segment, then bisect the two resulting segments)
Question 8.
The angle bisector of a 45° angle results in an angle of:
(a) 90°
(b) 30°
(c) 22.5°
(d) 15°
Solution:
(c) 22.5°
Constructions and Tilings Class 7 Assertion and Reason Questions
Instructions:
In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
1. Assertion (A): To construct a perpendicular bisector of a line segment XY, the radius of the arcs drawn from X and Y must be the same and greater than half the length of XY.
Reason (R): Any point equidistant from the endpoints of a line segment lies on its perpendicular bisector.
Solution:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
2. Assertion (A): It is impossible to construct a 40° angle using only a ruler and a compass, but possible to construct a 30° angle.
Reason (R): Using angle bisection, we can only construct angles that are halves of 90°, 60°, or their combinations.
Solution:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
3. Assertion (A): A regular pentagon cannot tile the floor without leaving gaps or overlapping.
Reason (R): The interior angle of a regular pentagon is 108°, and 108° is not a divisor of 360°.
Solution:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
4. Assertion (A) : To construct a line parallel to a given line l through a point P not on l, we can construct equal corresponding angles.
Reason (R) : If two lines are intersected by a transversal and the alternate interior angles are equal, then the lines are parallel.
Solution:
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
5. Assertion (A) : Equilateral triangles, squares, and regular hexagons are the only regular polygons that can tile a plane.
Reason (R) : These are the only regular polygons whose interior angles divide 360° evenly.
Solution:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
6. Assertion (A) : A 7 × 8 grid can be completely tiled using 2 × 1 domino tiles.
Reason (R) : The total number of unit squares (7 × 8=56) is an even number.
Solution:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
7. Assertion (A) : The perpendicular bisector of a segment XY also acts as the angle bisector of the angle formed by two points A and (where AX = AY and BX = BY) on either side of the segment.
Reason (R) : The perpendicular bisector is the locus of all points equidistant from the endpoints of the segment.
Solution:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Constructions and Tilings Class 7 Fill in the blanks
Question 1.
A perpendicular bisector is a line that cuts a line segment into two equal parts at ………….
Answer:
90°
Question 2.
The basic tools required for geometric constructions are a ………… and a ………….
Answer:
compass, straightedge
Question 3.
Tiling in mathematics involves covering a surface or plane with one or more geometric shapes, called …………, without overlaps or gaps.
Answer:
tiles
Question 4.
Any point that is equidistant from the endpoints of a line segment lies on the ………….
Answer:
perpendicular bisector
Question 5.
Regular tilings are arrangements of identical shapes that cover a plane completely without any ………… or ………….
Answer:
gaps, overlaps
Question 6.
Using angle bisection, an angle of 90° can be bisected to construct a ………… angle.
Answer:
45°
Question 7.
The angle formed by the intersection of a perpendicular bisector and the line segment is a ………… (or 90°).
Answer:
right angle
Question 8.
In a “checkerboard argument” for tiling, each 2 × 1 tile covers exactly one ………… square and one ………… square.
Answer:
white, black
Question 9.
The number of tiles required to cover a surface is calculated by dividing the total area of the surface by the ………….
Answer:
area of one tile
Question 10.
To construct a copy of an angle, a ………… is used to measure and transfer the distance between the arms of the angle.
Answer:
compass
Constructions and Tilings Class 7 True or False
Question 1.
Only regular polygons can be used for tiling a plane without gaps.
Answer:
False
Question 2.
A 65.5° angle can be constructed using only a compass and straightedge.
Answer:
False
Question 3.
A line segment has only one perpendicular bisector.
Answer:
True
Question 4.
When constructing a perpendicular bisector, the radius of the arcs above and below the line must be different.
Answer:
False
Question 5.
Tiling involves covering a surface with shapes, allowing for small gaps.
Answer:
False
Question 6.
An angle bisector divides an angle into two equal parts.
Answer:
True