# Ex.10.1 Q1 Practical Geometry Soltion - NCERT Maths Class 7

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## Question

Draw a line, say \(AB,\) take a point \(C\) outside it. Through \(C, \)draw a line parallel to \(AB\) using ruler and compasses only.

## Text Solution

**What is known?**

A line \(AB\) and a point \(C\) outside it.

**To construct:**

A line through \(C\) parallel to \(AB\) using ruler and compasses.

**Reasoning:**

Draw a line \(AB\) and take a point \(C\) outside it. Draw line \(AB\) by using ruler and compasses, follow the steps given below.

**Steps:**

** Steps of construction** –

- Draw a line, \(AB,\) take a point \(C\) outside this line. Take any point \(P\) on \(AB\). Join \(C\) to \(P\).
- Taking \(P\) as centre and a convenient radius draw an arc intersecting line \(AB\) at \(D\) and \(PC\) at \(E.\)
- Taking \(C\) as the centre and the same radius in previous step, draw an arc \(FG\) intersecting \(PC\) at \(H. \)
- Adjust the compasses up to the length of \(DE\). Without changing the opening of compasses and taking \(H\) as the centre, draw an arc to intersect arc \(HG\) at point \(I.\)
- Join the point \(C\) and \(I\) to draw a line \(L.\)

This is the required line \(L\) which is parallel to \(AB.\)