Geometric Constructions Quiz – Geometry (10 Questions)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

Standards: G-CO.D.12, G-CO.D.13 · Level: Grade 10 Geometry

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What this Compass and Straightedge Constructions quiz checks

• Constructions use only a compass and a straightedge with no marks.
• The perpendicular bisector needs a compass opening larger than half the segment.
• An angle bisector arc construction works because of SSS congruent triangles.
• A circle's radius fits around it six times: the inscribed hexagon has side r.
• Every second vertex of the hexagon gives an inscribed equilateral triangle of side r√3.

The 10 questions of the quiz

1. A regular hexagon is inscribed in a circle of radius 4. How long is each side?
2. Which tools are allowed in a compass and straightedge construction?
3. To construct the perpendicular bisector of a segment, the compass opening must be
4. An angle of 88° is bisected by construction. How large is each half?
5. In the angle bisector construction shown, which two segments are congruent because they are radii of the same arc?
6. How is an equilateral triangle inscribed in a circle using the hexagon?
7. A square is inscribed in a circle of radius 9. How long is its diagonal?
8. Which idea is used to construct a line parallel to a given line through a point?
9. A point lies on the perpendicular bisector of segment AB. What is true of the point?
10. What is the central angle of each side of a regular hexagon?

After the quiz

Missed a question? Reread the Compass and Straightedge Constructions lesson, then take the quiz again. Next, solve the Geometry worksheet on Compass and Straightedge Constructions, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.