Geometry Constructions Quiz – Free PDF

Contents

This geometry constructions quiz asks 10 multiple-choice questions on geometric constructions, and each answer comes with a short explanation.

Ten multiple-choice questions check the key ideas of compass and straightedge constructions: bisectors, perpendicular and parallel lines, and inscribed polygons. Four questions include a figure. Each explanation shows why the answer is correct and which mistake to avoid. Read every option before you choose, because the wrong answers use common slips such as confusing the radius with the side length.

GeometryCommon Core: G-CO.D.12 · G-CO.D.13

🎯 Geometric Constructions – Geometry math quiz

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Question 1

Which tool is used to mark a length equal to a given segment without measuring?

A Compass

B Straightedge

C Protractor

D Ruler

Question 2

M is the midpoint found by constructing the perpendicular bisector of AB. If \(AB=12\text{ cm}\), what is \(AM\)?

Perpendicular bisector of AB meeting AB at M.

A \(12\text{ cm}\)

B \(3\text{ cm}\)

C \(6\text{ cm}\)

D \(24\text{ cm}\)

Question 3

Angle ABC measures \(78^{\circ}\). After constructing its bisector, what does each half measure?

A \(78^{\circ}\)

B \(156^{\circ}\)

C \(19.5^{\circ}\)

D \(39^{\circ}\)

Question 4

A regular hexagon is inscribed in a circle of radius 9 cm. What is the length of each side?

Regular hexagon inscribed in a circle.

A \(4.5\text{ cm}\)

B \(9\text{ cm}\)

C \(18\text{ cm}\)

D \(54\text{ cm}\)

Question 5

Which method constructs a square inscribed in a circle?

A Step around the circle six times with the radius

B Draw a diameter, then construct its perpendicular bisector

C Bisect the radius twice

D Draw two equal chords at random

Question 6

Why is triangle ABC equilateral?

Triangle ABC built with arcs centered at A and B.

A AC and BC are radii of arcs drawn with width AB

B Angle C was bisected with a compass

C The compass was opened to half of AB

D AB is parallel to a line through C

Question 7

A line through P is constructed parallel to line l by copying an angle. Which angle pair is copied?

A Vertical angles

B A linear pair

C Corresponding angles

D Complementary angles

Question 8

Point P lies on the perpendicular bisector of segment XY, and \(XY=14\). If \(PX=9\), what is \(PY\)?

A \(14\)

B \(7\)

C \(9\)

D \(18\)

Question 9

What is the measure of each central angle of an inscribed regular hexagon?

A \(30^{\circ}\)

B \(90^{\circ}\)

C \(120^{\circ}\)

D \(60^{\circ}\)

Question 10

In copying an angle, which compass width is used to mark the last arc?

Copying angle A to a new angle at D.

A The radius AP

B The distance PQ

C The distance AD

D Any convenient width

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards G-CO.D.12 and G-CO.D.13 cover making formal constructions and inscribing regular polygons.
The compass copies lengths; the straightedge only draws lines through two points and is never used to measure.
The perpendicular bisector of a segment is built with equal arcs wider than half the segment, centered at both endpoints.
A regular hexagon inscribed in a circle has side length equal to the radius.
Joining every other vertex of the hexagon gives an equilateral triangle; perpendicular diameters give a square.