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Construction, Locus
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Constructions using straightedge and compass are an important part of
every standard geometry curriculum. The solutions to problems in this
section require students to describe the process of construction and/or
the result of a series of constructions.
- Related Resources
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Interactive resources from our Math Tools project:
Geometry: Construction and Loci
The closest match in our Ask Dr. Math archives:
High School: Constructions
NCTM Standards:
Geometry Standard for Grades 9-12
Access to these problems requires a Membership.
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Angle Trisection with a Carpenter's Square
- Annie Fetter
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Geometry, difficulty level 3. Prove how a carpenter's square can be used to trisect an angle.
... more>>
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A Carpenter's Trisection
- Annie Fetter
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Geometry, difficulty level 3. Explain whether or not the given method of trisecting an angle, using only a carpenter's square, really works.
... more>>
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The Center of Gravity of a Quadrilateral
- Annie Fetter
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Geometry, difficulty level 3. Find the center of gravity of a quadrilateral.
... more>>
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Construct an Isosceles Triangle
- Annie Fetter
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Geometry, difficulty level 2. Give at least three different ways to construct an isosceles triangle (a construction can be repeated over and over and in this case will always yield an isosceles triangle).
... more>>
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Constructing a Tangent
- Annie Fetter
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Geometry, difficulty level 3. Explain why this construction of a tangent works.
... more>>
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A Construction Puzzle
- Annie Fetter
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Geometry, difficulty level 3. Given angle PQR and point Y in the interior of the angle, construct XZ so that X lies on QP, Z lies on QR, and Y is the midpoint of XZ.
... more>>
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Point P Perambulates
- Annie Fetter
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Geometry, difficulty level 3. Find the length of the path of a vertex of an equilateral triangle as that triangle rotates around the inside of a square.
... more>>
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Proving PD
- Annie Fetter
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Geometry, difficulty level 3. AOD is a diameter of the circle with center O. B is any point on the
circle that isn't A or D. A tangent is drawn to the circle at point B.
A line is drawn through O parallel to AB, meeting the tangent at P.
Prove that PD is a tangent to the circle.
... more>>
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