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6. Join XY. XY is the required line segment such that XY = AB – CD.

A 7.1 cm B C 3.9 cm D

l
X 3.2 cm Y 3.9 cm Z
7.1 cm
(
By measuring, we find that XY = 3.2 cm which is equal to AB CD− )
i.e., 7.1 cm – 3.9 cm = 3.2 cm
Construction of Perpendicular Lines or Line Segments

We know that the term ‘perpendicular’ means ‘at right angles’. So, two lines m
(segments or rays) are said to be perpendicular to each other if they intersect
and form a right angle (90°) between them. 90° 90°
Construction of a Perpendicular to a Line Through a Point on it 90° 90° l

Let us draw a perpendicular to the given line AB through a point P on it.
Steps of construction:
1. Let AB be a straight line. Q
2. Take point P on AB.
3. With P as a centre and convenient radius draw a semicircle
to intersect AB at X and Y.
4. Now place the compass on X and draw an arc with radius A X P Y B
greater than PX or PY.
5. Again, place the compass on Y and draw an arc with same radius as above.
6. Both the arcs intersect at Q.
7. Join PQ.
8. QP is perpendicular to XY. We, write it as QP ⊥ XY
Construction of a Perpendicular to a Line Through a Point Outside the Line

Let us take a line MN and a point P outside it, and
Draw a line through P, perpendicular to MN.

Steps of construction:
1. Let MN be a given line and P be a point outside it.
2. Take P as the centre and a suitable radius, draw an arc that
intersects MN at A and B.
3. Now take A and B as centres and draw arcs with radius greater
than AL and BL to the opposite side of point P.
4. Join PQ that intersects MN at L. Thus, PL is perpendicular on MN.
Therefore, ∠PLM = ∠PLN = 90°

335 Construction of Basic Geometrical Shapes