Back to Make geometric constructions — Problem 2 · Task Set 12

Exercises: Make Formal Geometric Constructions

Work through each section in order. For construction problems, show all compass arcs and straightedge marks — do not erase construction lines. For multiple-choice problems, choose the best answer.

Grade 9·22 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-co-d-12

Work through problems with immediate feedback

Fluency Practice

Each problem tests your knowledge of the six standard constructions. Identify the correct step, tool use, or construction outcome.

$Perpendicular bisector construction: segment AB with arcs from A and B intersecting at P above and Q below, with line PQ crossing AB perpendicularly at midpoint M.$

The diagram shows a perpendicular bisector construction on segment AB. Points P and Q are the two intersection points of the arcs drawn from A and B. Which statement correctly justifies why line PQ is perpendicular to AB?

P and Q were drawn by hand to look symmetrical, so the line between them appears perpendicular.

P and Q are each equidistant from A and B, so both lie on the perpendicular bisector of AB by the equidistance theorem.

The arcs cross exactly at the midpoint of AB, so the line through the crossing points is perpendicular.

A and B are the same distance from the line PQ, which means PQ must be vertical.