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Browse High School Euclidean/Plane Geometry
Stars indicate particularly interesting answers or
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Selected answers to common questions:
Pythagorean theorem proofs.
- Trisecting a Line [01/30/1998]
How do I trisect a line using only a straightedge and compass?
- Trisecting a Line Segment [08/13/1999]
How can I measure one-third of a line of an unknown length using a
compass and a straightedge?
- Trisecting an Angle [06/15/1999]
I've come up with a method of approximately trisecting any angle. Can you
tell me how accurate it is?
- Trisecting an Angle [06/17/2000]
I believe I have a simple straightedge and compass construction that
trisects any angle except a right angle, but have not been able to write
- Trisecting an Angle [4/16/1996]
I can bisect an angle easily but I can't trisect it perfectly. Would you
please send me instructions?
- Trisecting an Angle: Proof [6/3/1996]
Is there a proof for how to trisect an angle?
- Trisecting Angles [03/10/1998]
An angle of 180/n, for n a positive integer not divisible by 3, can be
- Trisecting a Right Angle [12/16/1996]
An explanation of how to trisect a 90 degree angle, plus some
- Trisecting How's and Which's [01/20/2015]
An adult wonders if trisectable angles share some common construction steps — and how to determine their trisectability in the first place. Doctor Jacques lays out the requirements.
- Two Circles, Four Tangents, Collinear Midpoints [12/20/1998]
Given two circles that do not touch there are four distinct tangents
common to both circles. Prove that the midpoints of the tangents are
- Two-column Proof [5/24/1996]
Theorem: tangent segments from a point outside a circle to a circle have
- Two-Column Proof About Kites [11/09/1999]
Can you help me understand a proof about perpendicular lines and
congruent triangles in a kite?
- Two Column Proof of a Theorem [08/12/1998]
Write a two-column proof and give numbered statements with reasons....
- Two-Column Proof of Congruence [05/16/2000]
How can I complete this two-column geometry proof?
- Two-Column Proof: Parallel Tangents [03/08/2002]
Prove that tangents to a circle at the endpoints of a diameter are
- Two-column proofs [12/18/1994]
I am writing on behalf of my daughter Mel who is a sophomore in high
school. She is having a real problem with proofs. In particular two
column proofs. Can you explain the steps to prove geometric figures?
- Two Discs, One Rotating [7/5/1996]
Two circular discs have radii 8 cm and 28 cm. The larger disc is fixed
while the smaller disc rolls around the outside of the larger...
- Two Interpretations of Dimensionality in Geometric Figures [03/16/2004]
A line is 1 dimensional, a square or rectangle is 2 dimensional, and a
cube is 3 dimensional. My question is what if you throw in parabolas
or circles or the absolute value function, etc.? A circle is kind of
like a parabola, but it is very much like a square, so I am thinking
it is 2-dimensional. My conclusion is that the only 1 dimensional
object is a straight line, and a point is 0 dimensional, but I am not
confident that I am correct. Can you please clear this up for me?
- Two Problems on Tangents [07/09/1998]
How can you show that the arc and the angle formed by two tangents are
supplementary? Find the radius of circle O, given the following...
- Two Slopes, and Two Ways to Average Them [01/06/2016]
An adult has questions about the validity of a colleague's simple
method to average slopes — and about simplifying his own, more
involved approach. With sketches, trigonometric identities, and
conjugate products, Doctor Peterson explains the methods, and shows
- Two Triangle Problems [6/11/1996]
One angle of a triangle is trisected... Find the shortest side.
- Unproven Fundamentals of Geometry [05/18/1999]
What are some important postulates or axioms that geometry cannot exist
without, but cannot prove, either?
- Using Relative Primes [12/07/1996]
Given a floor 105 tiles wide and 135 tiles long, how many tiles will a
diagonal drawn from one corner to the opposite corner intersect?
- Using Vectors in Geometry and Physics [07/10/1998]
How do you use vectors in problems about medians, areas, and acceleration
- Vector Proof [01/17/1999]
Prove that given P, Q, R, and S (any 4 non-collinear points), with A and
B the midpoints of PR and QS respectively, then PQ + RS = 2 AB...
- Vector Proof: Parallelogram Diagonals [01/20/1999]
Use vectors to prove that the diagonals of a parallelogram bisect each
other and the line joining the midpoints of two sides of a triangle...
- Vectors of Parallelograms and Octagons [07/28/1998]
ABCDEFGH is a regular octagon and AB = p and BC = q. Express AH in terms
of p and q...
- Vertical angles [11/15/1994]
Are vertical angles congruent in Euclidean geometry?
- Vertical Angles [10/27/1996]
What are vertical angles?
- Visualizing Skew Lines [05/16/2002]
What do you call lines that are not parallel but don't intersect?
- Voronoi Diagrams [12/12/2000]
On a Voronoi diagram, how do you know which lines and which parts of
those lines you need?
- A Way to Remember What 'm' and 'b' Mean in Slope-Intercept Form [02/01/2004]
An interesting memory trick to help you remember how to graph a linear
equation in slope-intercept form.
- What Are Proofs? [08/12/1997]
I am homeschooling and do not understand proofs. Can you help me out?
- What does Angle ABC Equal? [3/5/1995]
A triangle, ABC, is obtuse angled at C. The bisectors of the exterior
angles at A and B meet BC and AC produced at D and E respectively. If
AB=AD=BE, then what does angle ABC equal?
- What Does It Mean for Angles to be Coterminal? [09/06/2007]
Find one positive angle and one negative angle that are coterminal
with an angle having measure 11 pi over 4.
- What is a Jordan Curve? [06/07/2006]
What is a simple definition of a Jordan curve I can give my 5th graders?
- What is a point? [8/26/1996]
Define a point, please.
- What Is a Theorem and Why Are They Important? [08/15/1997]
I don't understand how theorems help us learn.
- What is Dimensional Analysis? [11/26/2001]
What is dimensional analysis and how does it work?
- What is Geometry For? [03/01/2002]
What is geometry really for?