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Browse High School Constructions
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- 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
- 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 [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
- 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
- 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
- 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.