Question

AB and CD are parallel. EF is the translation of AB. Is EF parallel to CD? Justify. What does this prove about the effect of translations on parallel lines?

Answer 1

Yes, EF is parallel to CD. Translation is the simple slide of a shape, therefore it doesn't have an effect on parallel lines.

Answer 2

Answer with explanation:

It is given that, two segments or two lines, AB and CD are parallel.

When we translate a line by some numeric value either horizontally right or left vertically up or down,either it will move downward or upward.

So, line AB when translated either Upward or Downward ,becomes EF.

So, translated line EF will be Parallel to AB.

Also, AB ║CD.------------(1)

As, EF ║AB.--------(2)

From (1) and (2)

EF ║ AB ║CD

⇒Two lines parallel to same line are parallel to each other.

⇒Translated line will be parallel to Original line and the line parallel to original line.