Construction of line parallel to given line, through point not on line

### Transcript

Construction of a line parallel to a given line, through a point not on the line Let’s take an example 1. Given a line l with point A not on it We need to draw a line parallel to line l, passing through point A 2. Mark point B on the line l Join AB 3. With B as center, and any radius, draw an arc intersecting l at C, and AB at D 2. Mark point B on the line l Join AB 3. With B as center, and any radius, draw an arc intersecting l at C, and AB at D 5. Open compass to length CD 6. Now, with E as center, and compass opened the same radius as before, draw an arc intersecting the previous arc at F 7. Draw a line m passing though A & F Thus, m is the line parallel to l, and passing though point A ∴ l ∥ m Justification From figure, we see that ∠ DBC = ∠ FAE as we have drawn them using the same radii. Now, for lines l and m ∠ DBC and ∠ FAE are alternate interior angles, and they are equal ∴ l ∥ m

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.