Ask Dr. Math

High School Archive

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.

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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.

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 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?

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.

Why Cubed? [11/27/2001]

Why do we use "cubed" for the volume of a figure?

Why is K Used as an Abbreviation for Area? [11/29/2004]

Many textbooks use the letter K to represent area in formulas, instead of A. Do you know why that is?

Why Learn Geometric Proofs? [02/27/2002]

Why are we taught geometric proofs if the vast majority of us will never use them?

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