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NCERT Solutions for Class 7th Maths Chapter 6 Construction of a Line Parallel to the Given Line — Figure it Out

Book page 148 Updated on2026-09-19

Q1.
Construct 4 pairs of parallel lines in different orientations.
Answer

Repeat the copy-the-corresponding-angle construction four times, choosing a different slant for the given line each time.

PairGiven line mTransversal lWhat you copy
1HorizontalSlanting up-rightThe angle at A onto B
2VerticalSlanting down-rightThe angle at A onto B
3Slanting up-rightHorizontalThe angle at A onto B
4Slanting down-rightVerticalThe angle at A onto B
Why it happens: the construction never refers to "horizontal" or "vertical". It only says: equal corresponding angles with respect to a transversal. That statement is true whatever the page is turned to, so the same steps work in every orientation.
Check it yourself: measure the perpendicular distance between the two lines at two widely separated places. For a true pair of parallels the two distances are equal.
Q2.
Construct the following figure.
STABHZUCGYVDFEXW
The eight-pointed star, page 148.
Answer

The figure is eight congruent rhombi arranged around one centre. Each rhombus has one vertex at the centre and the opposite vertex at a star tip. Opposite sides of a rhombus are parallel — that is where the parallel-line construction is used.

Eight rhombi meet at the centre with no gap and no overlap
Angle of each rhombus at the centre = 360° ÷ 8 = 45°
Check: 8 × 45° = 360° ✓

In a rhombus, adjacent angles add to 180°, so the angle at a star tip
= 180° − 45° = 135°
  1. Mark the centre O. Draw a line through O and its perpendicular, then bisect each right angle. That gives 8 rays, 45° apart.
  2. With one compass opening, cut the eight rays at S, T, U, V, W, X, Y, Z — all the same distance from O.
  3. Take two neighbouring rays OS and OT. Through T construct the line parallel to OS, and through S the line parallel to OT. The two lines meet at a point — call it A. Then O, S, A, T are the four corners of the first rhombus.
  4. Repeat for each of the eight neighbouring pairs of rays. The eight inner points A, B, C, … H appear.
  5. Ink the rhombus outlines; shade alternate rhombi if you want the star effect of the book.
Why it happens: a rhombus is a parallelogram with all four sides equal. Because all eight rays are cut at the same distance, every rhombus has the same side length; because the rays are 45° apart, every rhombus has the same corner angle at O. So all eight are congruent, and the design has 8-fold rotational symmetry.
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