Playing with Constructions class 6 solutions

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Class 6 Maths Chapter 8: Playing with Constructions (Solved)

Class 6 Maths Chapter 8: Playing with Constructions (Solved)

Note: Refer to your textbook for diagrams and figures. See image numbers mentioned below to match with visuals.

8.1 Artwork and Use of Compass

Q: What is the shape formed by all points at a fixed distance from a point?
It’s a circle. The fixed point is the centre and the fixed distance is the radius (See Fig. 8.2 on page 188).
Q: Can we recreate Fig. 8.1 using ruler and compass?
Yes, it becomes easier with proper placement of compass tips and measured radius. Try multiple trials for symmetrical curves.

8.2 Squares and Rectangles

Q: Properties of Rectangles?
  • Opposite sides are equal (R1)
  • All angles are 90° (R2)
Q: Properties of Squares?
  • All sides are equal (S1)
  • All angles are 90° (S2)
Q: Is a rotated square still a square?
Yes, because its lengths and angles remain unchanged. (See Fig. 8.3 and Fig. 8.4)

8.3 Constructing Squares and Rectangles

Construct a square of side 6 cm:
  1. Draw line PQ = 6 cm
  2. Draw perpendicular at P and mark PS = 6 cm
  3. Draw perpendicular at Q and mark QR = 6 cm
  4. Join RS to complete square PQRS (Refer image steps on page 195–196)
Construct rectangle of sides 4 cm × 6 cm
Follow similar steps ensuring opposite sides are equal and angles are 90°.

8.4 Exploration in Rectangles

Q: Where are X and Y closest/farthest?
They are closest when equally far from A and B. Farthest when diagonally placed (i.e., like AC or BD). Use ruler or compass to confirm (See page 197–199).
Q: Construct rectangle into 2 or 3 identical squares:
Choose side AF, mark equal parts, and use perpendiculars to complete rectangle. Use compass to copy lengths (See page 200–201).

8.5 Diagonals of Rectangles and Squares

Q: What do diagonals of rectangle do?
They divide opposite angles into equal parts. Diagonals are equal. Measure and verify (See Fig. on page 203).

Construct:

1. Rectangle with angle split 60°–30°: Draw base, draw angle 60°, draw perpendiculars, complete figure (page 205–207)
2. Rectangle with side 5 cm and diagonal 7 cm: Use compass from D to get B at intersection of perpendicular and arc (page 208–210)

8.6 Points Equidistant from Two Points

Construct the House Figure:
  1. Draw base 5 cm, construct sides and roof using compass (r = 5 cm)
  2. Use arcs from B and C to find point A
  3. Join A to B and C, then draw arc from A through B and C (See pages 211–214)

Try These

  • Construct a house with 7 cm sides
  • Recreate ‘A Person’, ‘Wavy Wave’, ‘Eyes’ using compass (Refer Artwork section)
  • Try creating square with circular hole and square with curves (Page 202–203)

Summary

  • Circle = set of points at same distance (radius) from centre
  • Compass can draw circle and arcs precisely
  • Use rough diagrams for planning
  • Rectangles/squares can be constructed with given sides or diagonal