Question 3

What condition is necessary for AE and BF to be equal? In this situation, what is the relationship between AB and CD? What can you conclude

about parallel lines with regard to the distance between them? Use the word perpendicular in your answer.

Answer:

In order for line AE to equal line BF, m/DFB and m/CEA must both be 90°. When this occurs, line AB does not intersect line EF: the two lines are parallel. line AE and line BF represent the perpendicular distances between line AB and line CD. When the two lines are parallel, the perpendicular distance between them is the same throughout their length.

Step-by-step explanation:

Plato Sample Question

When the two lines are parallel, then the perpendicular distance between them is the same throughout their length.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

In order for line AE to equal line BF, Angle DFB and Angle CEA must both be 90°.

When this occurs, line AB does not intersect line EF then the two lines are parallel.

Thus the line AE and line BF represent the perpendicular distances between line AB and line CD.

When the two lines are parallel, then the perpendicular distance between them is the same throughout their length.

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