7th construction of parallel lines
Answers
Step-by-step explanation:
Steps to Construct Parallel Lines
To construct a line parallel to the other line from an external point we require a ruler and a compass and the following steps are followed:
Given: A line segment AB and a point P that lies out of the line segment AB
To construct a line that is perpendicular to line AB that passes through point P.
Step 1: Choose any point X on the line segment AB and join it to point P as shown.
Construction of Parallel Lines-Step 1
Step 2: With X as center and any suitable radius draw an arc cutting the line segment PX at point M and AB at point N respectively.
Construction of Parallel Lines-Step 2
Step 3: With P as center and radius as used in previous step draw an arc EF cutting the line segment PX at point Q as shown.
Construction of Parallel Lines-Step 3
Step 4: With Q as center and same radius as before, draw an arc cutting the arc EF at R as shown below.
Construction of Parallel Lines-Step 4
Step 5: Join R and P to draw a line segment CD as shown.
Construction of Parallel Lines-Step 5
The line segment CD is the required line parallel to the line segment AB and passes through the point P.
To verify whether the line segment that is constructed is parallel to line segment AB, connect the points E, Q and M, N as described below:
Construction of Parallel Lines-Step 6
In the triangle EPQ and XMN,
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