Question

Draw a line segment $AB=8cm$. Take any point $P$ outside it . Using scale and compasses, draw a line through $P$ parallel to $AB$.

Answer 1

STEPS OF CONSTRUCTION:

STEP 1 : Draw $AB=8cm$

STEP 2 : Take any point $P$ outside $AB$ and take any point $Q$ on $AB$ and $PQ$.

STEP 3 : Take $Q$ as center and any radius draw an arc intersecting $AB$ at X and $QP$ at $Y$.

STEP 4 : With the same radius and center at $P$ draw an arc opposite side of arc $XY$ intersecting $QP$ at $M$.

STEP 5 : With the help of compasses measure arc $XY$ and with $M$ as center draw an arc intersecting the previous arc at $N$.

STEP 6 :Draw a line $CD$ joining the points $P$ and $N$ . $CD$ is the line parallel to $AB$.

$\angle PQB=\angle CPQ$ (alternate interior angles)

Hence $AB$ and $CD$ are two transversal lines with $PQ$ transversal line.