Question
Draw any $\triangle\text{ABC}.$ Bisect side $AB$ at $D$. Through $D$, draw a line parallel to $BC$, meeting $AC$ in $E.$ Measure $AE$ and $EC.$
✓
Answer
Steps of construction:
Step I: We first draw a triangle $A B C$ with each side $=6 cm$.
Steps to bisect line $AB:$
Step I: Draw an arc from $A$ on either side of line $A B$.
Step II: With the same radius as in the previous step, draw an arc from $B$ on either side of $AB$ intersecting the arcs drawn in the previous step at $P$ and $Q $.
Step III: Join $PQ$ cutting $A B$ at $D . P Q$ is the perpendicular bisector of $A B$.
Parallel line to $B C$ :
Step I: With $B$ as centre, draw an arc cutting $B C$ and $B A$ at $M$ and $N$, respectively.
Step II: With centre $D$ and the same radius as in the previous step, draw an arc on the opposite side of $A B$ to $c u t ~ A B$ at $Y$.
Step II: With centre $Y$ and radius equal to $MN$ , draw an arc cutting the arc drawn in the previous step at $X$ .
Step III: Join $XD$ and extend it to intersect $AC$ at $E.$
Step IV: $DE$ is the required parallel line.
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