### Mathematics Class VII

Integers
Fractions and Decimals
Exponents and Powers
Algebraic Equations
Simple Linear Equations
Lines and Angles
Comparing Quantities
Congruence of Triangles
Rational Numbers
Perimeter and Area
Data Handling
Practical Geometry
Symmetry
Visualising Solid Shapes

# 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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