See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Triangles and Other Polygons
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Pythagorean theorem proofs.
- Naming Corresponding Parts of Congruent Figures [04/23/2003]
Given triangle OPS congruent to triangle TQR, name the corresponding
sides and angles of the two triangles.
- Naming Polygons [5/30/1995]
Could you please give me a complete list of polygon names from 3 - 100?
- Naming the Isosceles Triangle [09/23/1998]
How did the isosceles triangle receive its name?
- Nonagon or Enneagon? [02/06/2003]
Is 'enneagon' really the correct name for a 9-sided polygon?
- Number of Points in a Star [7/16/1996]
Is there a way to predict the number of points in a star given only the
internal angle of the corners?
- One- and Two-sided Polygons [12/07/1999]
Can you explain what a monogon and a digon are?
- On Polygons, Polygons within Polygons, and Definitions [07/22/2010]
If we cut one polygon out of the interior of another, is the resulting shape a polygon?
Doctor Peterson gives a curious student a better definition than he found in his book,
pointing out the importance of separating polygons from their interiors -- and of
experimenting with definitions.
- Origami Equilateral Triangle [04/26/2001]
How can I create an equilateral triangle from a piece of paper using only
- Origin, Meaning of 'Hypotenuse' [9/13/1996]
What is the origin and meaning of the term "hypotenuse"?
- Parallelogram Perimeter [10/01/1997]
The diagonals of a parallelogram are 10 and 24 in length. If one side of
the paralellogram is 13, what is the perimeter?
- Pentagram [12/08/2001]
Is a five-pointed star on a flag a decagon? Or just five triangles?
- Perimeter of Two Similar Objects [2/16/1996]
Why do you lose area in a 4 x 12 rectangle as compared to an 8 x 8
square? Each has the same perimeter.
- Picture of Icosahedron [7/31/1996]
Do you have a picture of an icosahedron?
- Pipe Needed for Natural Gas Line [09/03/1997]
Two houses are 130 metres apart at distances of 55 and 105 metres...
- Placing Coins That Touch [8/7/1996]
How many 20-cent coins can you put around a 20-cent coin so that all of
- Pole in a Box [02/09/1999]
Can a pole 6.5m long fit into a truck with dimensions of 3m, 3.5m, and
- Polygon Diagrams [05/11/2003]
I would like to see pictures of polygons with 11, 12, 13, 14, and 15
- Polygon Names [09/18/2001]
Why is a 3-sided polygon called a triangle instead of a tri-gon? Why is a
4-sided polygon called a quadrilateral instead of a tetragon, when all
the others are ___-gons? Why is there not a single consistent term?
- Polygon Names II [12/11/2003]
Why is the triangle named "triANGL"', unlike all the other polygons, which have names like "quadriLATERAL" or "pentaGON"?
- Polygons and Circles [4/3/1996]
Is a circle a polygon? Why or why not?
- Polygons, Infinite Sides, and Circles [04/03/1997]
Can a regular polygon with an infinite number of sides be a circle?
- Polyominoes [09/08/1997]
I am using polyominos, but I do not know how to tell my dad what they
are. How can I tell him so he will know?
- Proof of Pythagorean Theorem: Pythagoras' Reasoning [02/23/1998]
I would like to know how Pythagoras reasoned his theorem.
- Proofs with Isosceles Triangles [10/28/1998]
What are altitudes, angle bisectors, and medians? How do you prove that
in an isoseles triangle, the altitude is a median and an angle bisector?
- Properties of Equilateral Triangles [07/20/1998]
If ABC is equilateral and AD is one of its heights, what are the measures
of the angles? Is ADB equal to ADC? If AB = 2 find BD and AD.
- Prove Triangles are Similar [12/16/1995]
How do you prove two triangles are similar?
- Pythagorean Theorem [1/19/1995]
What is the Pythagorean Theorem?
- Pythagorean Theorem [7/19/1995]
How come a^2 + b^2 = c^2?
- Pythagorean Theorem [5/14/1996]
What is the Pythagorean theorem?
- The Pythagorean Theorem: A Modern Proof [04/14/1997]
I know that the Pythagorean Theorem works and I can show how it works,
but why does it work?
- Pythagorean Theorem Legend [01/31/2009]
Is there a Sioux Indian legend that refers to the Pythagorean Theorem?
- Pythagorean Theorem Proof by Brodie Explained [03/15/2000]
Could you give me a step-by-step explanation of Dr. Scott Brodie's proof
of the Pythagorean theorem given at the cut-the-knot website?
- Pythagorean Theorem Proof: Four Right Triangles [10/7/1996]
I don't understand the Pythagorean Theorem.
- Pythagorean Triples [04/14/1997]
Why can't all the numbers in a Pythagorean triple be prime?
- Quadrilateral Classification: Definition of a Trapezoid [01/15/1997]
What is the correct definition of a trapezoid, and why?
- Quadrilateral Patterns [03/06/1997]
What is the formula that gives the number of quadrilaterals within a
square grid when you increase the square grid by one unit on each side?
- Quadrilaterals [8/31/1995]
What is 4-sided and has no equal angles?
- Ratio and proportion [12/5/1994]
I need extra help in ratio and proportion.
- Ratio of Sides and Ratio of Areas [02/11/1999]
If the sides of a triangle are in the ratio of 1:7, what is the ratio of
their areas? What about for other shapes?
- Ratios and Geometry [10/29/1998]
An airplane flying at 33,000 feet has a visibility of 100 miles. What
percent of the total land area to the horizon is visible?