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Browse High School Triangles and Other Polygons
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Area of an irregular shape.
Classifying quadrilaterals.
Heron's formula.
Polygon diagonals.
Pythagorean theorem proofs.
Triangle congruence.
 Constructing a Segment [09/26/1999]

Given a 1" segment and a 2.5" segment, how can you find a segment of
length sqrt(2.5)" using only a compass and a straightedge?
 Constructing a Square [12/25/1998]

Given any four points, construct a square such that each side or
extension passes through one point.
 Constructing a Triangle [08/20/1999]

How can you construct a triangle with 3 differentsize segments?
 Constructing a Triangle Given the Medians [01/01/2001]

How can I construct a triangle ABC given AM, BN, and CP, the respective
medians from the vertices A, B, and C?
 Constructing Polygons [06/03/1998]

How do you construct a regular pentagon and a regular decagon? Can you
construct a regular ngon?
 Constructing the Orthocenter [01/27/1999]

How do you construct the orthocenter of a triangle?
 Construct Polygon Given One Side [12/03/2001]

How can you construct a polygon, given one side?
 Converse of the Pythagorean Theorem [02/14/2003]

What is the converse of the Pythagorean theorem?
 Cosine Addition Formula [12/13/1997]

How can you prove the addition formula for cosine by using right
triangles?
 Counting Collinear Sides [04/12/2013]

A student wonders how to count the sides of a polygon that has degenerate vertices.
Citing Wikipedia and MathWorld, Doctor Peterson teases out the various conventions.
 Counting Diagonals [03/14/1998]

How many diagonals can be drawn for a polygon with n sides?
 Counting Intersections of Diagonals in Polygons [03/08/2000]

Can you help me find an equation for the maximum number of intersections
of the diagonals in a polygon?
 Counting Rectangles Cut By a Diagonal [06/15/1999]

How can we find an equation for the number of unit squares that are cut
by a line going from corner to corner on a rectangle?
 Counting Sides by Counting Diagonals [06/04/2002]

How can I find the number of sides in a polygon, given the number of
diagonals?
 Covering Paper using Index Cards [10/24/2001]

What is the maximum area of an 8"x13" sheet of paper that you can cover
by using seven 3"x5" standard index cards?
 CrossCornering a Shape to Make it Square [12/19/2002]

We lay out a building that is 30' x 40' and crosscorner it to see if
it is 'square,' but there is a 6' difference. What is the equation to
find how far to move one side to make the shape 'square'?
 Curious Property of a Regular Heptagon [04/06/2001]

How can I prove that in a regular heptagon ABCDEFG, (1/AB)=(1/AC)+(1/
AD)?
 Cutting a Circle out of a Square [2/14/1996]

What is the area (to the nearest square centimeter) of the largest circle
that can be cut from a square piece of sheet metal 73cm. on each side?
Explain how you determined this.
 Cutting a Square into Five Equal Pieces [07/12/1999]

How can you divide a square cake into five equal parts, cutting through
the center point?
 Cutting a Triangle into Two Congruent Triangles [10/06/1998]

How do you cut a triangle into two congruent equilateral triangles with
the minimum number of cuts?
 Cutting Carpet [9/9/1996]

Two pieces of carpet are to be used to cover a floor. You are allowed to
make just one cut in one of the two pieces...
 Cyclic Quadrilateral [05/22/2000]

For an isoscles trapezium ABCD with AB paralled to DC and AB less than
CD, how can we prove that ABCD is a cyclic quadrilateral?
 Cyclic Quadrilaterals [8/30/1996]

A cyclic quadrilateral touches a circle at each vertex. What angles do
these points make with the centre of the circle?
 Cyclic Trapezoid [01/17/2002]

PQ is a diameter; AB is a chord parallel to PQ. If PQ=50cm and AB= 14cm,
find PB.
 Defining Exterior Angles of Polygons [06/24/2004]

My math teacher says the sum of the exterior angles of a triangle is
900 degrees (360*3  180). I think that the sum is 360 degrees. Who
is correct?
 Definition of Opposite Sides [01/18/2001]

What is the formal definition of 'opposite sides' of a polygon? Does a
regular pentagon have opposite sides? Does a concave polygon have
opposite sides? How can we define it consistent with our intuition?
 Degenerate/Nondegenerate Figure [10/27/2001]

We need to know what a nondegenerate circle is. (We're trying to decide
whether this is a model of incidence geometry, but don't know the
definition.)
 Degenerate Triangle [09/03/2003]

Isn't a degenerate triangle really just a line segment?
 De Longchamp's Point [09/21/2000]

What is De Longchamp's point, and how is it used?
 Derivation of Law of Sines and Cosines [11/02/1997]

How do you derive the law of sines and the law of cosines?
 Derivations of Heron's Formula [11/24/1998]

How is Heron's formula (Hero's formula) derived?
 Derivations of Pi and a Polygon of Degree n [3/4/1995]

I am curious about the derivation of pi and the formula for deriving a
polygon of degree n. Can you help?
 Deriving the Distance Formula from the Pythagorean Theorem [03/23/2003]

How does one derive the distance formula from the Pythagorean theorem?
 Deriving the Law of Cosines [04/01/1998]

Will the Pythagorean Theorem work with a nonright triangle?
 Deriving Trilinear Coordinates [05/18/1999]

How do you derive the trilinear coordinates of the orthocenter of a
triangle?
 Desargues' Theorem and SSASS [12/15/1998]

What is the main theory behind Desargues' Theorem? Also, is SSASS a valid
method for proving two quadrilaterals are congruent?
 Determinants and the Area of a Triangle [12/14/1998]

Given a triangle with vertices (A,B), (C,D), and (E,F), how do you find
the area in determinant form?
 Determine if Point is in Rectangle [5/29/1996]

What formula will allow me to determine whether a specified point lies
within a polygon (rectangle  4 points)?
 Determining Area of a Lot of Land [08/20/2003]

We are trying to figure out the square footage for a lot that I own.
 Determining If a Given Point Lies inside a Polygon [12/27/2005]

I have a finite number of points that constitute a polygon, and a
point p(x,y). I want to know if point p lies inside the polygon.
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