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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?

The Angle Bisector and Equal Side Ratios, Now by Similarity [01/15/2016]
Bisecting the angle of one triangle vertex puts its adjacent legs in proportion with segments on the opposite leg that result from extending that bisection. How do you prove this proportionality using similarity? By extending the angle bisector even further, Doctor Floor shows the way.

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?

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