Class 6 Maths Playing with Constructions Notes

Class 6 Maths Playing with Constructions Notes

Class 6 Maths – Chapter: Playing with Constructions

1. Introduction

“Playing with Constructions” is all about drawing geometric shapes accurately using basic tools: compass, ruler, protractor, and pencil. It helps students understand lines, angles, triangles, and circles practically.

2. Tools and Their Uses

  1. Ruler – Measure and draw straight lines
  2. Compass – Draw arcs and circles
  3. Protractor – Measure and draw angles
  4. Divider – Transfer distances

3. Important Constructions

  1. Bisecting a Line Segment
    • Step 1: Draw a line segment AB
    • Step 2: With A and B as centers, draw arcs of equal radius intersecting at two points
    • Step 3: Join the intersection points to meet the line → Midpoint of AB
  2. Bisecting an Angle
    • Step 1: Draw an angle ∠ABC
    • Step 2: Draw an arc cutting both sides of the angle
    • Step 3: With intersection points as centers, draw arcs intersecting each other
    • Step 4: Join vertex to intersection → Bisector of ∠ABC
  3. Constructing Perpendicular from a Point on a Line
    • Step 1: Draw a line and mark a point P on it
    • Step 2: Draw arcs from P cutting the line at two points
    • Step 3: Draw arcs from intersection points above P to meet
    • Step 4: Join P to intersection → Perpendicular line
  4. Constructing Perpendicular from a Point Outside a Line
    • Step 1: Draw a line and mark point P outside it
    • Step 2: With P as center, draw an arc cutting the line at two points
    • Step 3: Draw arcs from these points to intersect
    • Step 4: Join P to intersection → Perpendicular line
  5. Constructing Triangles Using SSS / SAS / RHS Rules
    • SSS: Given three sides
    • SAS: Given two sides and included angle
    • RHS: For right-angled triangle given hypotenuse and one side
  6. Drawing Circles of Given Radius
    • Using a compass, mark the center and draw a circle with required radius

4. Examples

Example 1 – Bisect a Line Segment AB = 6 cm

  • Draw arcs from A and B with radius > 3 cm → Join intersections → Midpoint found

Example 2 – Bisect ∠60°

  • Draw arcs cutting both rays → Draw arcs from intersections → Join vertex → 30° angle

Example 3 – Triangle Construction (SSS)

  • Given sides 5 cm, 6 cm, 7 cm → Draw base 7 cm → Draw arcs from endpoints with remaining sides → Intersection = 3rd vertex → Join

5. Practice Questions (50 Mixed)

Part A – MCQs – 15 Questions

  1. Which tool is used to draw arcs?
  2. Bisector of an angle divides it into ___ parts
  3. Midpoint of a line segment divides it into ___ parts
  4. Perpendicular from a point on line creates ___ degree angle
  5. Compass is used to draw …
  6. Ruler is used to …
  7. Which triangle construction needs RHS rule?
  8. SSS means …
  9. SAS means …
  10. Angle bisector of 90° = ?
  11. Drawing a circle requires …
  12. Divider is used to …
  13. Perpendicular from outside a line meets the line at …
  14. Using arcs intersection to draw lines is called …
  15. Tool to measure angles = ?

Part B – Fill in the Blanks – 10 Questions

  1. Midpoint divides a line segment into ___ equal parts
  2. Angle bisector divides angle into ___ equal angles
  3. Compass helps to draw ___ and ___
  4. Ruler helps to draw ___
  5. Protractor measures ___
  6. SSS stands for ___
  7. SAS stands for ___
  8. RHS rule is used for ___ triangle
  9. Perpendicular from a point outside a line is drawn using ___
  10. Triangle can be constructed using ___, ___, ___

Part C – True/False – 5 Questions

  1. Compass can measure angles (False)
  2. Ruler can measure lines (True)
  3. Angle bisector divides angle into equal parts (True)
  4. RHS rule is for right-angled triangles only (True)
  5. Divider is used to draw angles (False)

Part D – Match the Following – 5 Questions

Column AColumn B
31. Compassa) Draw arcs and circles
32. Rulerb) Draw straight lines
33. Protractorc) Measure angles
34. Dividerd) Transfer distances
35. RHS Rulee) Right-angled triangle

Part E – Short Answer / Problem Solving – 15 Questions

  1. Bisect a line segment of 8 cm
  2. Bisect a 60° angle
  3. Draw perpendicular from a point on line
  4. Draw perpendicular from a point outside a line
  5. Construct triangle with sides 5 cm, 6 cm, 7 cm
  6. Construct triangle with sides 6 cm, 5 cm and included angle 60°
  7. Draw circle of radius 5 cm
  8. Draw angle bisector of 90°
  9. Draw perpendicular from mid-point of line 10 cm
  10. Construct right triangle with hypotenuse 6 cm, one side 4 cm
  11. Draw circle touching a line at one point
  12. Draw triangle using SAS
  13. Draw triangle using RHS
  14. Draw triangle using SSS
  15. Bisect a 120° angle

Answers – Class 6 Maths: Playing with Constructions

Part A – MCQs (Answers)

  1. Compass
  2. Two equal parts
  3. Two equal parts
  4. 90°
  5. Arcs and circles
  6. Draw straight lines
  7. Right-angled triangle
  8. Side-Side-Side
  9. Side-Angle-Side
  10. 45°
  11. Compass + center + radius
  12. Transfer distances
  13. At 90° (perpendicular)
  14. Using intersection of arcs
  15. Protractor

Part B – Fill in the Blanks (Answers)

  1. Two
  2. Two
  3. Arcs, circles
  4. Straight lines
  5. Angles
  6. Side-Side-Side
  7. Side-Angle-Side
  8. Right-angled
  9. Compass and arcs
  10. SSS, SAS, RHS

Part C – True/False (Answers)

  1. False
  2. True
  3. True
  4. True
  5. False

Part D – Match the Following (Answers)

Column AColumn B
31. Compassa) Draw arcs and circles
32. Rulerb) Draw straight lines
33. Protractorc) Measure angles
34. Dividerd) Transfer distances
35. RHS Rulee) Right-angled triangle

Part E – Short Answer / Problem Solving (Answers)

  1. Bisect a line segment of 8 cm:
  • Draw line AB = 8 cm
  • With radius > 4 cm, draw arcs from A and B intersecting above and below line
  • Join intersections → Midpoint at 4 cm
  1. Bisect a 60° angle:
  • Draw ∠AOB = 60°
  • Draw arc cutting both rays at C and D
  • Arcs from C and D intersect at E
  • Join O to E → Two 30° angles
  1. Perpendicular from point on line:
  • Let P be on line
  • Draw arcs from P cutting line at A and B
  • Draw arcs from A and B intersecting above P at Q
  • Join P to Q → perpendicular
  1. Perpendicular from point outside line:
  • Let P outside line
  • Draw arc from P cutting line at A and B
  • Draw arcs from A and B intersecting at Q
  • Join P to Q → perpendicular
  1. Triangle with sides 5 cm, 6 cm, 7 cm (SSS):
  • Draw base = 7 cm
  • Draw arcs from endpoints with 5 cm and 6 cm radii
  • Intersection = third vertex → Join points
  1. Triangle with sides 6 cm, 5 cm, included angle 60° (SAS):
  • Draw one side 6 cm
  • Draw 60° at one end
  • With radius 5 cm, draw arc → intersection = third vertex → Join
  1. Circle of radius 5 cm:
  • Draw center O
  • With compass radius = 5 cm, draw circle
  1. Bisect 90° angle:
  • Arc intersects rays at C and D
  • Arcs from C and D intersect at E
  • Join vertex to E → two 45° angles
  1. Perpendicular from midpoint of 10 cm line:
  • Midpoint at 5 cm
  • Draw arcs from midpoint above and below line
  • Join midpoint to intersections → perpendicular
  1. Right triangle with hypotenuse 6 cm, one side 4 cm (RHS):
  • Draw hypotenuse 6 cm
  • Draw perpendicular side 4 cm from one end
  • Complete triangle → Right-angled at perpendicular
  1. Circle touching line at one point:
  • Draw line
  • Draw circle with radius = perpendicular distance from center to line
  1. Triangle using SAS:
  • Draw side, included angle, and other side → complete triangle
  1. Triangle using RHS:
  • Right-angle triangle with given hypotenuse and side → draw perpendicular → complete triangle
  1. Triangle using SSS:
  • Draw base → arcs from endpoints with remaining sides → join → complete triangle
  1. Bisect 120° angle:
  • Draw arcs from vertex intersecting rays at C and D
  • Draw arcs from C and D intersecting at E
  • Join vertex to E → two 60° angles