Draw a line segment $AB$ of $4 \,cm$ in length. Draw a line perpendicular to $AB$ through $A$ and $B$,respectively. Are these lines parallel?

(N/A) Given: $A$ line segment $AB$ of length $4 \,cm$.
Required: To draw perpendiculars to $AB$ through points $A$ and $B$,respectively.
Steps of construction:
$1.$ Draw a line segment $AB = 4 \,cm$.
$2.$ At point $A$,construct a $90^{\circ}$ angle using a compass and ruler to draw a perpendicular line $CD$.
$3.$ At point $B$,construct a $90^{\circ}$ angle using a compass and ruler to draw a perpendicular line $EF$.
$4.$ Since both lines $CD$ and $EF$ are perpendicular to the same line segment $AB$,they make interior angles of $90^{\circ}$ with $AB$.
$5.$ The sum of the interior angles on the same side of the transversal $AB$ is $90^{\circ} + 90^{\circ} = 180^{\circ}$.
$6.$ Therefore,the lines $CD$ and $EF$ are parallel to each other.