Construction Of A Line Parallel To A Given Line, Through A Point Not On The Line

We need to construct it using ruler and compass only.

Step 1: Draw a line PQ and take a point R outside it.

Step 2: Take a point J on the line PQ and join it with R.

Step 3: Take J as a centre and draw an arc with any radius which cuts PQ at C and JR at B.

Step 4: Now with the same radius, draw an arc taking R as a centre.

Step 5: Take the measurement of BC with compass and mark an arc of the same measurement from R to cut the arc at S.

Step 6: Now join RS to make a line parallel to PR.

∠ARS = ∠BJC, hence RS ∥ PQ because of equal corresponding angles.

This concept is based on the fact that a transversal between two parallel lines creates a pair of equal corresponding angles.

Remark: This can be done by taking alternate interior angles instead of corresponding angles.

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