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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 n-gon?

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.

16-sided Regular Polygon [07/31/2001]
How can I construct a 16-sided polygon?

Angle-Side-Side Does Not Work [11/12/2001]
Can you give me a construction to show that Angle-Side-Side 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 Zero-Degree 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 45-degree Angle [06/02/1998]
How do you construct a 45-degree 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 One-Degree 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 semi-circles.

Constructing a Triangle [08/20/1999]
How can you construct a triangle with 3 different-size 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 non-overlapping 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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