Geometric Constructions: Geometry Math Quiz – PDF Download
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?
ACompass
BStraightedge
CProtractor
DRuler
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?
AStep around the circle six times with the radius
BDraw a diameter, then construct its perpendicular bisector
CBisect the radius twice
DDraw two equal chords at random
Question 6
Why is triangle ABC equilateral?Triangle ABC built with arcs centered at A and B.
AAC and BC are radii of arcs drawn with width AB
BAngle C was bisected with a compass
CThe compass was opened to half of AB
DAB 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?
AVertical angles
BA linear pair
CCorresponding angles
DComplementary angles
Question 8
Every point on the perpendicular bisector of AB is
Acloser to A than to B
Btwice as far from A as from B
Cthe same distance from A and from B
Dexactly at distance AB from A
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.
AThe radius AP
BThe distance PQ
CThe distance AD
DAny convenient width
🎉 Quiz complete!
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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.
