Playing with Constructions — Class 6 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Playing with Constructions" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Playing with Constructions" — 8 important questions with detailed answers for CBSE…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

What are the tools used in practical geometry and what do they do?
Construct a perpendicular to a line at a given point using ruler and compass.
How do you construct an angle of 60° using ruler and compass?
Bisect an angle of 80° using compass and ruler.
Construct a perpendicular from a point to a line using compass and ruler.
What is meant by congruent line segments?
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
What are the tools used in practical geometry and what do…	✓ Solved
Construct a perpendicular to a line at a given point usin…	✓ Solved
How do you construct an angle of 60° using ruler and comp…	✓ Solved
Bisect an angle of 80° using compass and ruler.	✓ Solved
Construct a perpendicular from a point to a line using co…	✓ Solved
What is meant by congruent line segments?	✓ Solved

Showing 6 of 8 questions

Q1: What are the tools used in practical geometry and what do they do?

Practical geometry uses specific instruments for accurate constructions Step 1: Ruler - used to draw straight lines and measure distances Step 2: Compass - used to draw circles and arcs, and to mark equal distances Step 3: Set square - used to draw angles like 90°, 45°, 60°, 30° Step 4: Protractor - used to measure angles and draw angles of any measure Final Answer: Ruler (for straight lines), Compass (for arcs/circles), Set square (for standard angles), Protractor (for angle measurement)

Q2: Construct a perpendicular to a line at a given point using ruler and compass.

Steps to construct a perpendicular at a point on a line Step 1: Draw a line AB and mark point P on it Step 2: Using compass with P as centre, mark equal distances on both sides - points X and Y Step 3: With compass more than half of XY, draw arcs above and below the line from X and Y Step 4: Let these arcs intersect at point C and D Step 5: Draw a line through C and D passing through P Step 6: CD is perpendicular to AB at P (CD ⊥ AB) Final Answer: A perpendicular line is constructed at point P

Q3: How do you construct an angle of 60° using ruler and compass?

Steps to construct 60° angle Step 1: Draw a ray OA Step 2: Place compass at O with any radius, mark an arc on OA at point B Step 3: With same radius and B as centre, draw another arc intersecting the first arc at C Step 4: Join O and C Step 5: Angle AOC = 60° Step 6: This works because triangle OBC is equilateral (OB = BC = OC) Final Answer: Angle of 60° is constructed

Q4: Bisect an angle of 80° using compass and ruler.

Steps to bisect an 80° angle Step 1: Draw angle AOB of 80° Step 2: With O as centre, draw an arc that cuts OA at P and OB at Q Step 3: With P as centre and radius more than half PQ, draw an arc inside the angle Step 4: With Q as centre and same radius, draw another arc inside the angle Step 5: Let these arcs intersect at point R Step 6: Draw ray OR Step 7: OR bisects angle AOB. Angle AOR = Angle BOR = 40° Final Answer: The angle is bisected; each part = 40°

Q5: Construct a perpendicular from a point to a line using compass and ruler.

Steps to construct perpendicular from point to line Step 1: Draw a line AB and point P outside the line Step 2: With P as centre, draw an arc intersecting AB at two points X and Y Step 3: With X as centre and radius more than half of XY, draw an arc below the line Step 4: With Y as centre and same radius, draw another arc intersecting the first arc at Q Step 5: Draw line PQ Step 6: PQ is perpendicular to AB Final Answer: Perpendicular from point P to line AB is constructed

Q6: What is meant by congruent line segments?

Congruent line segments are segments that have equal length Step 1: Two line segments are congruent if they can be placed one over the other exactly Step 2: If AB = CD in length, then AB is congruent to CD (written as AB ≅ CD) Step 3: Using compass, we can compare and mark equal distances Step 4: This allows us to construct segments equal to a given segment Final Answer: Congruent line segments have equal length and can coincide completely

Showing 6 of 8 questions. Visit the full page for complete solutions.