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5. To construct a line passing through point that is parallel to the line AB, Han constructed the perpendicular bisector of AB and then drew line CD.

Is CD guaranteed to be parallel to AB? Explain how you know.

5 To construct a line passing through point that is parallel to the line AB Han constructed the perpendicular bisector of AB and then drew line CD Is CD guarant class=

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MrRoyal

Parallel lines are simply lines that extend in both directions, and do not intersect.

Line CD is guaranteed to be parallel to AB

From the attachment, we have the following observations

  • The line drawn from CD to AB is perpendicular to AB
  • Points C and D are on the same straight horizontal level

This means that, the line drawn from CD to AB:

  • Is perpendicular to CD
  • is perpendicular to AB

If a line is perpendicular to two other lines, then the two other lines are parallel.

So, we can conclude that:

Lines CD and AB are parallel

Read more about parallel and perpendicular lines at:

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