Class 6 Maths · Original EZT practice
Playing with Constructions (Class 6 Chapter 8): summary and practice
A compass and a ruler are all you need to draw perfect shapes. This chapter turns doodling into geometry: constructing squares and rectangles, exploring what their diagonals do, and finding every point that is equally far from two given points. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 22 October 2026:
1. Artwork and the two instruments
A geometric construction draws an exact figure using only a ruler (straight lines) and a compass (circles and equal distances). A compass fixes a distance exactly, so constructions beat measuring with a scale.
2. Squares and rectangles
A rectangle has four right angles and equal opposite sides; a square has all four sides equal. So a rectangle needs two measurements, a square just one - draw a base, erect perpendiculars with compass arcs, mark the side, join.
3. Rectangle patterns and diagonals
With perimeter fixed at 20 cm the whole-number rectangles 9x1, 8x2, 7x3, 6x4, 5x5 have areas 9, 16, 21, 24, 25 - the square wins. Diagonals of any rectangle are equal and bisect each other; a square's also meet at right angles.
4. Points equidistant from two points
Every point equally far from A and B lies on one straight line: the perpendicular bisector of AB, which cuts AB in half at a right angle. Swing equal arcs from A and B to build it.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Name the instruments
Choose the method: Constructions use exactly two tools.
EZT practice question
Which two instruments are used in the constructions of this chapter, and what is each for?
Show the worked solution
- The ruler draws straight lines and fixes lengths.
- The compass draws circles and copies distances exactly.
- No protractor - right angles come from compass arcs.
Answer: A ruler and a compass.
Check: A compass fixes a distance exactly, which is why constructions are more precise than measuring with a scale alone.
Watch for this: Do not reach for the protractor - in a true construction, right angles are built with arcs, not measured.
Now try it yourself
Why is a compass copy more exact than measuring?
Check your answer
It transfers the distance directly.
No reading of scale marks means no reading error.
Count the measurements
Choose the method: Equal sides and right angles cut the information needed.
EZT practice question
How many measurements do you need to construct a square? And a rectangle?
Show the worked solution
- A square has four equal sides and four right angles.
- One side length fixes everything.
- A rectangle has two different side lengths - length and breadth - so it needs two.
Answer: One for a square; two for a rectangle.
Check: A square of side 6 cm: draw a 6 cm base, erect perpendiculars, mark 6 cm on each, join the tops - one number drove it all.
Watch for this: Do not measure all four sides - equal sides and right angles make that redundant.
Now try it yourself
A square has perimeter 24 cm. What is its side?
Check your answer
6 cm.
24 / 4 = 6, since all four sides are equal.
Read a rectangle's sides
Choose the method: Opposite sides of a rectangle are equal.
EZT practice question
A rectangle is 7 cm long and 4 cm broad. What are the lengths of its four sides?
Show the worked solution
- Opposite sides of a rectangle are equal.
- Two sides are 7 cm (the lengths).
- The other two are 4 cm (the breadths).
Answer: 7 cm, 4 cm, 7 cm, 4 cm.
Check: Perimeter check: 7 + 4 + 7 + 4 = 22 cm, and 2 x (7 + 4) = 22 cm - consistent.
Watch for this: Adjacent sides differ - only OPPOSITE sides are equal.
Now try it yourself
Perimeter of that rectangle?
Check your answer
22 cm.
2 x (7 + 4) = 22.
Maximise area for a fixed perimeter
Choose the method: List the rectangles; the square wins.
EZT practice question
Which whole-number rectangle of perimeter 20 cm has the greatest area?
Show the worked solution
- Half the perimeter is 10, so sides are 9x1, 8x2, 7x3, 6x4, 5x5.
- Areas: 9, 16, 21, 24, 25 sq cm.
- The largest is 25 sq cm - the 5 cm x 5 cm square.
Answer: The 5 cm x 5 cm square, area 25 sq cm.
Check: Each pair sums to 10, so each perimeter is 20 cm; the areas climb as the sides get closer - the square is the limit.
Watch for this: Fixed perimeter does NOT mean fixed area - the 9x1 rectangle holds only 9 sq cm against the square's 25.
Now try it yourself
Area of the 8x2 rectangle with the same perimeter?
Check your answer
16 sq cm.
8 x 2 = 16, less than the square's 25.
State the diagonal facts
Choose the method: Measure both diagonals and their crossing.
EZT practice question
What is true of the diagonals of every rectangle, and what extra holds for a square?
Show the worked solution
- Draw both diagonals of a rectangle and measure: they are equal.
- They bisect each other - each cuts the other into two equal halves.
- In a square they also meet at right angles.
Answer: Equal and bisecting each other; in a square, also perpendicular.
Check: Fold or measure to verify - the halves match, and only the square gives the right angle where they cross.
Watch for this: A general rectangle's diagonals do NOT meet at right angles - that is the square's extra.
Now try it yourself
True or false: a rectangle's diagonals always meet at right angles.
Check your answer
False.
Only in a square (and a rhombus) do they.
Locate the equidistant points
Choose the method: Equal distances from A and B force one special line.
EZT practice question
A house must be equally far from two trees 10 m apart. Describe all possible spots.
Show the worked solution
- Points equidistant from A and B form the perpendicular bisector of segment AB.
- That is the line cutting the 10 m segment in half at a right angle.
- Any point on it works - the house can stand anywhere along that line.
Answer: Anywhere on the perpendicular bisector of the segment joining the trees.
Check: Every point on the perpendicular bisector is equidistant from A and B, and no point off it is - equal compass arcs from A and B meet exactly on that line.
Watch for this: The midpoint is only ONE such point - the whole perpendicular bisector qualifies.
Now try it yourself
A point is 4 cm from A and 4 cm from B. Where must it lie?
Check your answer
On the perpendicular bisector of AB.
Equidistant from both endpoints means exactly that line.
Try a mixed set
Choose a method or explanation before opening each answer.
1. Instruments for constructions?
Show answer and reason
Ruler and compass.
Ruler for lines, compass for exact distances.
2. Measurements for a square?
Show answer and reason
One - the side.
Four equal sides and four right angles.
3. Diagonals of a rectangle?
Show answer and reason
Equal and bisecting each other.
A square's diagonals also meet at right angles.
4. Points equidistant from A and B?
Show answer and reason
The perpendicular bisector of AB.
It cuts AB in half at a right angle.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Construct a square of side 5 cm with ruler and compass.
- List all whole-number rectangles with perimeter 16 cm and find their areas.
- Mark two points 6 cm apart and construct their perpendicular bisector.
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Questions about this practice page
- What is a geometric construction?
- Drawing an exact figure using only a ruler and a compass - the ruler for straight lines, the compass for copying distances and drawing arcs. No protractor: right angles are built with arcs.
- How do you construct a square of side 6 cm?
- Draw a 6 cm base, erect perpendiculars at both ends with compass arcs, mark 6 cm on each perpendicular, and join the two marks.
- What are the properties of a rectangle's diagonals?
- They are equal in length and bisect each other. In a square they also meet at right angles - that extra property does not hold for a general rectangle.
- What is the perpendicular bisector of a segment?
- The line that cuts the segment in half at a right angle. It is exactly the set of all points equidistant from the segment's two endpoints.
- Are these the NCERT exercise questions for Playing with Constructions (Class 6)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.