Draw a line segment AB of 4 cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?
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• To draw a line perpendicular to AB through A and B, respectively.
Use the following steps of construction.
- Draw a line segment AB = 4 cm.
- Taking 4 as centre and radius more than ½ AB (i.e., 2 cm) draw an arc say it intersect AB at E.
- Taking E as centre and with same radius as above draw an arc which intersect previous arc at F.
- Again, taking F as centre and with same radius as above draw an arc which intersect previous arc (obtained in step II) at G.
- Taking G and F are centres, draw arcs which intersect each other at H.
- Join AH . Thus, AX is perpendicular to AB at A. similarly, draw BY ⊥ AB at B.
Now,
we know that if two lines are parallel, then the angle between them will be 0° or 180°.
Here,
∠XAB = 90° [∴ XA ⊥ AB] and ∠YBA = 90°
[ ∴ YB ⊥ AB] ∠XAB + ∠YBA = 90° + 90° = 180° So, the lines XA and YS are parallel.
[since, it sum of interior angle on same side of transversal is 180°, then the two lines are parallel]
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