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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The Role of Postulates [03/29/2003]

Who decided what were postulates and what were theorems? Why is it okay that postulates aren't proven?

Rotating a Point [04/08/2003]

Find the image of a triangle with vertices A(0,1),B(-2,0),and C(-4,-5) under a rotation of 90 degrees counterclockwise about the origin. Is there a formula I can use instead of drawing a picture?

Rule of Three [01/23/2002]

How high above the surface of the earth must a person be raised to see 1/3 (one third) of its surface?

Scanning for Mountains [06/02/1999]

I am standing on a hill scanning the horizon to see a mountain. How high must the mountain be for high-tech optical equipment to be any use?

Sextant Theorem [05/13/2001]

What mathematical theorem is behind using a sextant, and can it be proved?

The Shortest Crease [12/29/1997]

A piece of paper is 6 units one side and 25 units on another side...

Short History of Geometry [09/15/2001]

Were there any people who helped to develop geometry besides Euclid?

Side Length of a Regular Octagon, Without Trigonometry [09/19/2003]

How can I find the length of one side of a regular octagon that has a (side-to-side) diameter of 16 feet, without using trigonometry?

Software for Displaying Geometric Shapes [9/29/1995]

Do you know where I could find a geometry program that would display geometric shapes?

Spherical Triangles [10/26/1996]

Why can't you use the Pythagorean formula to measure the distance between two points on Earth?

Spiral Baffle in a Cylinder [6/24/1996]

We have a cylinder, 48 inches in diameter, to put a spiral baffle inside... What would the radius be?

Square Peg, Round Peg [08/22/1997]

Which fits better, a square peg in a round hole, or a round peg in a square hole?

Sum of Two Arcs [01/30/2003]

Three points are taken at random on the circumference of a circle. What is the chance that the sum of any two arcs so determined is greater than the third?

Surface Area and Volume: Cubes and Prisms [05/27/1998]

What is the definition of surface area and volume? What are the differences and similarities between surface area and volume?

Symmetry Proof [09/27/2001]

Given an angle with vertex O and a point P inside the angle, drop perpendiculars PA, PB to the two sides of the angle, draw AB, and drop perpendiculars OC, PD to line AB. Then show that AC=BD.

Tangent of 90 Degrees [5/24/1996]

Why is the tangent of 90 degrees undefined?

Tanker Bearings [06/11/2000]

From ship A, the bearing of an oil tanker is 300 degrees; from ship B, 1000 m due west of A, the bearing of the tanker is 060 degrees. Is the oil tanker the same distance from A as from B?

Taping a Cylinder [01/29/2001]

If I want to wrap sticky tape around a cylinder to cover it, what is the relation between the diameter of the cylinder, the thickness of the tape, and the angle between the diameter of the cylinder and the length of the tape?

Theorems and Postulates [12/02/2006]

If SSS, SAS, and AAS are theorems, why do other books still use them as postulates?

Thinking About Proofs [09/24/1997]

How do you know what statement to write next in a proof? What reasons do you use?

Three Colors on a Plane [03/04/2003]

Given three colors, green, red, and blue, that must be painted onto a plane. The entire plane is to be covered. When the three colors are placed on the plane every straight line that can be drawn will pass through exactly two colors.

Three-dimensional Counterparts for Two-dimensional Objects [03/04/1998]

Three-dimensional counterparts for lines, polygons, perpendicular lines, and collinear lines.

A Three-Legged Stool [06/26/2001]

Why is a three-legged stool steady, while a four-legged stool can be wobbly?

Three Spheres in a Dish [08/04/1999]

What is the radius of a hemispherical dish if 3 spheres with radii of 10 cm are inside the dish and the tops of all 3 spheres are exactly even with the top of the dish?

Three Tapers and a Length [8/25/1995]

I have three tapers (or angles) that intersect with each other. Theoretically, if I were given the total length from 0 to Y and the total height 0 to X and of course the three angles, is it possible to calculate each angles length and height?

Tiling a Floor [06/30/1999]

How many square yards is a 12ft. by 15ft. room? How many 8" x 8" tiles would you need for a 30 sq. ft. room?

Traceable Mathematical Curves [10/27/1997]

Is there any way to tell just by looking if a curve is traceable or not? Is there some property of a curve that will tell you this? Do curves have formulas?

Translation [9/11/1996]

What does translation mean?

Trapezoid Diagonals and Midpoints of Parallel Sides [03/04/2002]

In a trapezoid, why are the midpoints of the parallel sides collinear with the intersection of the diagonals?

Triangle and Circle with same Center [7/8/1996]

An equilateral triangle and a circle have the same center... find the length of the side of the triangle.

Triangle and Circumscribed Circle [03/23/1998]

How can you find the radius of a circle circumscribed around any triangle given the three outside points of the triangle.

A Triangle in a Circle [05/26/2000]

Suppose you randomly place 2 points on the circumference of a circle. What is the probability that a 3rd point placed randomly on the circle's circumference will form a triangle that will contain the center of the circle?

Triangle in Randomly Colored Plane [10/28/2002]

Prove: Assume that all points in the real plane are colored white or black at random. No matter how the plane is colored (even all white or all black) there is always at least one triangle whose vertices and center of gravity (all 4 points) are of the SAME color.

Triangles within a Triangle [11/10/1996]

If multiple small equilateral triangles are drawn within a larger one, what is the relation between the number of small triangles lying on the base of the big triangle and the total number contained within the big triangle?

A Triangle with Three Right Angles [12/01/1999]

How can you make a triangle with three right angles?

Trisecting a Line [11/03/1997]

How would you trisect a line using a compass and a straight edge?

Trisecting a Line [01/25/1998]

Is it possible to trisect a line? (Using propositions 1-34, Book 1 of Euclid's elements.)

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?

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