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Browse High School Constructions
Stars indicate particularly interesting answers or
good places to begin browsing.
 Constructing Polygons [06/03/1998]

How do you construct a regular pentagon and a regular decagon? Can you
construct a regular ngon?
 Geometry Constructions with Compass and Straightedge [11/13/1998]

I need help constructing medians, angle bisectors, and perpendicular
bisectors of triangles.
 Simson Line [04/19/1999]

What is the Simson line?
 Tangent Circle Construction [12/02/1996]

Given a circle with two points inside it, construct another circle that
passes through the given points and is tangent to the given circle.
 16sided Regular Polygon [07/31/2001]

How can I construct a 16sided polygon?
 AngleSideSide Does Not Work [11/12/2001]

Can you give me a construction to show that AngleSideSide does not
prove two triangles congruent?
 Angle Trisection: Construction vs. Drawing [10/17/2001]

Has anyone ever divided an angle into three equal parts by construction?
I have been told it has not been accomplished.
 Apollonian Construction Problem [03/06/2001]

Given a line and two points A and B, construct a circle tangent to the
line and containing the two points.
 Apollonius' Problem [09/07/2000]

Given three circles, is it possible to construct a circle tangent to each
of them using only a compass and straightedge?
 Applying Euler's Methods [07/27/1999]

Questions about prime divisors, triangle constructions, decomposing
quartic polynomials, and rational roots.
 Arbelos Construction [03/10/2000]

Is there a Euclidean construction for the circles that are sandwiched in
the Arbelos?
 Attempt at Trisecting an Angle [11/08/1999]

Can the arcs of the two circles formed by the construction described be
the same length? Would this construction trisect the angle?
 Bisecting a ZeroDegree Angle [08/26/2003]

Can a zero degree angle be bisected?
 Classical Geometry [04/16/2002]

Let ABC be a triangle with sides a, b, c. Let h be the perpendicular
from A to a, and m the median from A to the midpoint of a. Construct
the triangle using only ruler and compass if you know A, h, m.
 Collapsible Compass [01/23/2002]

How did the early Greek mathematicians reproduce lengths with a
collapsible compass?
 Collapsible Compass [11/21/2003]

What is a collapsible compass, and when would you use one?
 Construct a Trapezoid [08/28/2001]

I tried drawing two lines that are parallel to each other for b and f,
and I drew c, but then d didn't fit. How do I construct this?
 Constructible Angles and Regular Polygons [04/17/1998]

What angles and regular polygons are constructible?
 Constructing a 45degree Angle [06/02/1998]

How do you construct a 45degree angle with only a compass and a
straightedge?
 Constructing a Line to Divide Area of a Triangle in Half [05/13/1998]

Cutting a triangle into two pieces of equal area by drawing a a line
parallel to one of the sides.
 Constructing an Ellipse [04/15/1997]

How do you draw an ellipse?
 Constructing Angles in Standard Position [12/11/2003]

I'm just learning to construct angles, and sometimes the answer key
shows the opposite of what I've constructed because I have started my
line pointing left instead of right. Does this make a difference?
 Constructing a OneDegree Angle [05/25/2000]

Is it possible to contruct a one degree angle using only a straightedge
and compass?
 Constructing a Regular Pentagon [2/21/1995]

We are interested in knowing how to construct a regular pentagon using a
compass and a straight edge.
 Constructing a Segment [09/26/1999]

Given a 1" segment and a 2.5" segment, how can you find a segment of
length sqrt(2.5)" using only a compass and a straightedge?
 Constructing a Segment of a Given Length [09/09/2005]

How do you construct a segment of length "the 8th root of 3" using a
compass and a straightedge?
 Constructing a Square [12/25/1998]

Given any four points, construct a square such that each side or
extension passes through one point.
 Constructing a Tangent to a Circle [03/19/1999]

Construct a tangent to a circle through a given point not on the circle.
 Constructing a Tangent to a Circle, Continued [03/26/2013]

The proof of a tangency construction leaves a couple puzzled. Doctor Peterson
explains how it relies on a property of angles inscribed in semicircles.
 Constructing a Triangle [08/20/1999]

How can you construct a triangle with 3 differentsize segments?
 Constructing a Triangle [09/29/2003]

Let x be a given angle. Let m and n be given lengths such that n > m.
How can I construct triangle ABC such that AB = m, AC + CB = n, and
the measure of angle ACB = x?
 Constructing a Triangle Given the Medians [01/01/2001]

How can I construct a triangle ABC given AM, BN, and CP, the respective
medians from the vertices A, B, and C?
 Constructing Axes of an Ellipse with Straightedge and Compass [01/23/2006]

Presented with the graph of an ellipse, is there a way to determine
the axes by using straightedge and compass?
 Constructing Tangents to Circles [05/08/2002]

How do you construct a line tangent to a circle through a point
outside the circle? How do you do it with only a straightedge?
 Constructing the Golden Ratio Using a Compass [12/30/2003]

I am writing a paper on the Golden Ratio and want to include a section
on how to construct the ratio on a line using a compass. Could you
please explain the construction?
 Constructing the Orthocenter [01/27/1999]

How do you construct the orthocenter of a triangle?
 Construct Polygon Given One Side [12/03/2001]

How can you construct a polygon, given one side?
 Construct Triangle ABC Given Altitude... [04/11/2002]

Given the altitude from vertex A, angle BAC, and the radius of the
circumscribed circle, construct triangle ABC.
 Creating Tangents to Circles [10/24/2007]

I know how to draw a tangent to a circle from a point outside the
circle. How can I create four distinct tangents that are common to two
nonoverlapping circles?
 Dividing a Line Segment into Seven Equal Parts [07/04/2003]

I need to divide a segment with the length of X into seven equal parts
using only a compass and straightedge. I also have to construct a line
segment the length square root of X.
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