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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 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 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.

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 collinear.

Two-column Proof [5/24/1996]
Theorem: tangent segments from a point outside a circle to a circle have equal lengths.

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 parallel.

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 their equivalence.

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 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?

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