Class 7 Maths Chapter 6 Constructions and Tilings worksheet with MCQs, short answer questions, practice questions and extra questions based on Ganita Prakash Part 2 for revision and exam preparation.
Worksheet
Grade 7 Mathematics
Ganita Prakash Part II
Chapter 6: Constructions and Tilings
Name:
Class:
Date:
Instructions:
- Read every question carefully.
- Use a ruler and compass wherever required.
- Show construction work clearly.
- Write your answers neatly.
- Do not look at the answer sheet until you finish the worksheet.
Section A – Multiple Choice Questions
1.A perpendicular bisector divides a line segment into:
2.The angle formed by two perpendicular lines is:
3.An angle bisector divides an angle into:
4.Each angle of an equilateral triangle measures:
5.A regular hexagon has:
6.A 2 × 1 tile covers:
7.Which instrument is mainly used to draw arcs during constructions?
8.A shape can tile a region when there are:
Section B – Fill in the Blanks
9.Bisection means dividing something into __________ equal parts.
10.A perpendicular line makes an angle of __________ with another line.
11.A line that divides an angle into two equal angles is called the __________.
12.A regular hexagon has __________ sides.
13.A regular hexagon can be constructed by using a compass with the __________ as the compass radius.
14.A 2 × 1 tile covers exactly __________ unit squares.
15.A 5 × 7 grid contains __________ unit squares.
Section C – True or False
16.A perpendicular bisector cuts a line segment into two equal parts.
Answer: __________
Answer: __________
17.Every point on the perpendicular bisector of XY is equally distant from X and Y.
Answer: __________
Answer: __________
18.A 5 × 7 grid can be completely tiled using 2 × 1 tiles.
Answer: __________
Answer: __________
19.An angle bisector divides an angle into two equal angles.
Answer: __________
Answer: __________
20.Every 2 × 1 tile covers one unit square.
Answer: __________
Answer: __________
21.A regular hexagon has six equal sides.
Answer: __________
Answer: __________
Section D – Short Answer Questions
22.What is a perpendicular bisector?
23.What is meant by bisection?
24.What is an angle bisector?
25.Why are equal-radius arcs used when constructing a perpendicular bisector?
26.Why does a point that is equally distant from X and Y lie on the perpendicular bisector of XY?
27.How can a 60° angle be constructed using a ruler and compass?
28.How can a 30° angle be constructed using angle bisection?
29.How can a 15° angle be constructed?
30.What is tiling?
Section E – Construction Questions
Use a ruler and compass for the following constructions.
31.Construct the perpendicular bisector of a line segment XY of suitable length.
Construction Work:
32.Construct a 90° angle at a given point on a line.
Construction Work:
33.Construct the bisector of a given angle.
Construction Work:
34.Construct a 60° angle.
Construction Work:
35.Construct a 30° angle.
Construction Work:
36.Construct a 15° angle.
Construction Work:
37.Construct a regular hexagon with side length 4 cm.
Construction Work:
38.Construct a regular hexagon with side length 5 cm.
Construction Work:
39.Draw a line l and mark a point P outside it. Construct a perpendicular to line l through P.
Construction Work:
Section F – Reasoning Questions
40.Will the line joining the two points at which the arcs meet, above and below XY, always be the perpendicular bisector of XY when XY is of any length and the arcs are drawn using a radius of any length?
41.Is it necessary to have the same radius for the arcs above and below XY while constructing the perpendicular bisector?
42.Is it necessary to construct the pairs of arcs above and below XY? Can both pairs be constructed on the same side?
43.While constructing one pair of intersecting arcs, is it necessary to use the same radii for both arcs?
44.If a point is equally distant from X and Y, where will the point lie?
45.Why does an equilateral triangle help us construct a 60° angle?
46.Why can a grid having an odd number of unit squares not be tiled completely with 2 × 1 tiles?
Section G – Tiling
47.Can a 4 × 6 grid be tiled using multiple copies of 2 × 1 tiles?
48.Can a 4 × 7 grid be tiled using 2 × 1 tiles?
49.Can a 5 × 7 grid be tiled using 2 × 1 tiles? Give a reason.
50.Is an m × n grid tileable with 2 × 1 tiles if both m and n are even? Give a general strategy.
51.Is an m × n grid tileable with 2 × 1 tiles if one of m and n is even and the other is odd? Give a general strategy.
52.Is an m × n grid tileable with 2 × 1 tiles if both m and n are odd? Give reasons.
53.Here is a 5 × 3 grid, with a unit square removed. Now it has an even number of unit squares. Is it tileable with 2 × 1 tiles?
54.How can black-and-white colouring help us decide whether a region can be tiled with 2 × 1 tiles?
55.If a region has 8 white squares and 6 black squares, can it be tiled using 2 × 1 tiles? Give a reason.
Section H – Higher Order Thinking
56.Construct at least four different angles and draw their bisectors.
Construction Work:
57.Construct an 8-petalled figure using 45° angles.
Construction Work:
58.Construct four pairs of parallel lines in different orientations.
Construction Work:
59.Construct a pointed arch using supporting lines and arcs.
Construction Work:
60.Construct a 6-pointed star using suitable geometric constructions.
Construction Work:
61.Draw a shape whose copies can tile the entire plane.
Drawing:
Answer Sheet
Use this section only after completing the worksheet.
| Q. | Answer |
|---|---|
| 1 | B – Two equal parts |
| 2 | C – 90° |
| 3 | A – Two equal angles |
| 4 | C – 60° |
| 5 | C – 6 equal sides |
| 6 | B – 2 unit squares |
| 7 | B – Compass |
| 8 | C – No gaps and no overlaps |
| 9 | two |
| 10 | 90° |
| 11 | angle bisector |
| 12 | six |
| 13 | side length |
| 14 | two |
| 15 | 35 |
| 16 | True |
| 17 | True |
| 18 | False |
| 19 | True |
| 20 | False |
| 21 | True |
| 22 | A line that divides a line segment into two equal parts and is perpendicular to it. |
| 23 | Dividing something into two equal parts. |
| 24 | A line that divides an angle into two equal angles. |
| 25 | Equal-radius arcs make the intersection points equally distant from the two endpoints. |
| 26 | Such a point lies on the perpendicular bisector of XY. |
| 27 | Construct an equilateral triangle using equal compass radii. The angle obtained is 60°. |
| 28 | Construct 60° and bisect it. |
| 29 | Construct 60°, bisect to 30°, then bisect 30° to obtain 15°. |
| 30 | Covering a region without gaps or overlaps. |
| 31 | Construction using equal-radius arcs from the two endpoints. |
| 32 | Construct a perpendicular at the given point. |
| 33 | Use equal arcs from the two arms and join their intersection to the vertex. |
| 34 | Construct an equilateral triangle. |
| 35 | Bisect a 60° angle. |
| 36 | Bisect a 30° angle. |
| 37 | Regular hexagon with side 4 cm. |
| 38 | Regular hexagon with side 5 cm. |
| 39 | Construct the perpendicular bisector of a segment on line l whose perpendicular bisector passes through P. |
| 40 | Yes, provided the arcs in each pair intersect. The intersection points are equally distant from X and Y. |
| 41 | No. The important condition is that each pair produces points equally distant from X and Y. |
| 42 | No. Both pairs can be constructed on the same side. |
| 43 | Yes, for the standard construction the two arcs of a pair use the same radius. |
| 44 | On the perpendicular bisector of XY. |
| 45 | Every angle of an equilateral triangle is 60°. |
| 46 | Each 2 × 1 tile covers two squares, so an odd number of squares cannot be completely paired. |
| 47 | Yes. 4 × 6 = 24, and 24 can be divided into pairs. |
| 48 | Yes. 4 × 7 = 28, which is even. |
| 49 | No. 5 × 7 = 35, which is odd. |
| 50 | Yes. Pair the rows or columns along the even dimension. |
| 51 | Yes. Use the even dimension to arrange the 2 × 1 tiles. |
| 52 | No. Odd × odd gives an odd number of unit squares. |
| 53 | Having an even number of squares is necessary but not always sufficient. Use the black-and-white colouring test. |
| 54 | Every 2 × 1 tile covers one black and one white square. Unequal numbers make tiling impossible. |
| 55 | No. There are 8 white and 6 black squares, so the numbers are unequal. |
| 56 | Construction activity. |
| 57 | Use eight equal 45° sectors around a point. |
| 58 | Copy corresponding angles to construct each parallel pair. |
| 59 | Use equal supporting lines and suitable arcs. |
| 60 | Use 60° constructions and symmetry to create the six points. |
| 61 | Examples include squares, equilateral triangles and regular hexagons. |
Teacher’s Note:Construction questions should be checked from the student’s actual ruler-and-compass construction. Minor differences in the appearance of arcs or orientation are acceptable when the required geometric relationships are correct.
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