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NCERT Solutions for Class 7th Maths Chapter 6 Steps of Construction to Copy an Angle — Figure it Out

Book page 147 Updated on2026-09-19

Q1.
Construct at least 4 different angles in different orientations without taking any measurement. Make a copy of all these angles.
Answer

Draw four angles freely — one narrow, one nearly a right angle, one wide, one opening downwards — and copy each by the arc-and-chord method.

  1. Draw the angle at A. Draw a fresh ray from X, pointing any way you like.
  2. Arc of radius r from A, cutting the arms at B and C.
  3. Same radius r from X, cutting the new ray at Z.
  4. Compass opened to BC; from Z cut the arc at Y.
  5. Join XY. Then ∠YXZ = ∠BAC.
Every copy rests on the same congruence:
AB = AC = XZ = XY = r  and  BC = YZ
⇒ ΔABC ≅ ΔXYZ (SSS) ⇒ ∠A = ∠X
Why it happens: the orientation of the copy does not matter at all. The construction fixes only the opening between the arms, never the direction they point. That is why the same three steps work for an angle opening left, right, up or down.
Tip: use the same radius r for the original and the copy. If you change it, the chord BC no longer matches the new arc and the copy will be wrong.
Q2.
Construct the Fig. 6.6.
Fig. 6.6, page 145.
Answer

Build one unit, then copy its angle again and again.

  1. Draw a horizontal base line and mark equally spaced points on it with the compass: V₁, V₂, V₃, … (all gaps equal).
  2. Draw the first unit: from V₁ draw two arms of equal length l with the chosen angle between them, and close it with an arc of centre V₁ and radius l.
  3. Copy that angle at V₂ using the arc-and-chord method, but place it upside down — the copy points the other way.
  4. Copy again at V₃ in the first orientation, and so on, alternating.
  5. Because all arms are of length l and all angles are copies of one angle, the units are congruent and the ends meet neatly.
Why it happens: a repeating pattern needs its unit to repeat exactly. Two measurements decide the unit — arm length and angle. The compass fixes the first; the copy-an-angle construction fixes the second. Alternating the orientation is just a flip; the unit itself is unchanged.
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