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?
Solution:
Steps of Construction
1. Construct a line segment AB = 4 cm
2. Consider 4 cm as centre and radius more than half of AB construct an arc which intersects AB at the point E
3. Considering E as centre and with same radius construct an arc which intersects the previous arc at the point G
4. Considering G and F as centres construct arcs that intersect each other at the point H
5. Now join AH.
6. AX is the perpendicular to AB at the point A
7. In the same way construct BY perpendicular to AB at the point B.
If two lines are parallel the angle between them will be 0° or 180°
∠XAB = 90° (as XA is perpendicular to AB)
∠YBA = 90° (as YB is perpendicular to AB)
We know that
∠XAB + ∠YBA = 90° + 90° = 180°
As the sum of interior angles on same side of transversal is 180°, the two lines are parallel
So XA and YS are parallel.
Therefore, the lines are parallel.
✦ Try This: Draw a line segment AB of 5 cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 11
NCERT Exemplar Class 9 Maths Exercise 11.3 Problem 2
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?
Summary:
A line segment AB of 4 cm in length is drawn. A line perpendicular to AB through A and B are drawn. Yes, XA and YS are parallel
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