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Word Problems

Browse Middle School Triangles and Other Polygons
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Classifying quadrilaterals.
    Polygon diagonals.
    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 origami-like folds?

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 them touch?

Pole in a Box [02/09/1999]
Can a pole 6.5m long fit into a truck with dimensions of 3m, 3.5m, and 4m?

Polygon Diagrams [05/11/2003]
I would like to see pictures of polygons with 11, 12, 13, 14, and 15 sides.

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?

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