Question

In the straightedge and compass construction of the perpendicular line below, how do you know that ef ⊥ gh?

a. ef and gh have equal lengths.
b. ef and gh intersect at a right angle.
c. ef and gh are parallel.
d. The angle formed by ef and gh is acute.

Answer 1

Line segment EF is perpendicular to line GH when they intersect at a right angle, marked by a 90° angle, which is the true indicator of perpendicularity in straightedge and compass constructions.

Step-by-step explanation:

In a straightedge and compass construction, line segment EF is perpendicular to line GH when they intersect at a right angle, meaning they form a 90° angle with each other. This is indicated by the presence of a square-shaped angle marker at the point of intersection in diagrams or, in actual constructions, through geometrical methods ensuring the angle is indeed a right angle. It is not the length of the line segments that matters, nor is it necessary that they are parallel or forming any other type of angle. Therefore, the correct answer is b. EF and GH intersect at a right angle.