Back to Make geometric constructions — Problem 5 · 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.

To construct a line through external point P parallel to line l, the key construction step is to copy a specific angle at P. Which angle must be copied and why?

Copy the angle between the transversal and line l at their intersection point Q, placing the congruent angle at P on the same side of the transversal — this creates equal corresponding angles, guaranteeing parallelism.

Copy the right angle (90 degrees) at the intersection of the transversal and l, so the new line is perpendicular to the transversal.

Copy the angle between the transversal and l at Q, placing it on the opposite side of the transversal at P — this creates alternate interior angles.

Draw a line through P that appears to run alongside l — no angle copying is needed because parallel lines look equidistant.