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Browse High School Euclidean/Plane Geometry
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Classifying quadrilaterals.
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 onethird 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
a proof...
 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
trisected.
 Trisecting a Right Angle [12/16/1996]

An explanation of how to trisect a 90 degree angle, plus some
constructions.
 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
collinear.
 Twocolumn Proof [5/24/1996]

Theorem: tangent segments from a point outside a circle to a circle have
equal lengths.
 TwoColumn 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 twocolumn proof and give numbered statements with reasons....
 TwoColumn Proof of Congruence [05/16/2000]

How can I complete this twocolumn geometry proof?
 TwoColumn Proof: Parallel Tangents [03/08/2002]

Prove that tangents to a circle at the endpoints of a diameter are
parallel.
 Twocolumn 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 2dimensional. 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 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
and velocity?
 Vector Proof [01/17/1999]

Prove that given P, Q, R, and S (any 4 noncollinear 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 SlopeIntercept Form [02/01/2004]

An interesting memory trick to help you remember how to graph a linear
equation in slopeintercept 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?
 When Does 2D Become 3D? [01/20/2003]

Is a piece of paper a 3D object when held up in space? Or is it a 2D
object in 3D space?
 When is the expression Q.E.D. used? [02/15/1999]

More on Q.E.D.
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