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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.
 What is Menelaus' Theorem? [11/15/1998]

Proof of Menelaus' Theorem, and discussion of its converse and Desargues'
Theorem.
 What is the Area Not Shared by the Circles? [3/3/1995]

Two circles intersect such that their centers and their points of
intersection form a square with each side equal to 3. What is the total
area of the sections of the square that are not shared by both circles?
 What Is the Length of PR? [01/01/2003]

In a circle of radius 6, a triangle PQR is drawn having QR=8 and
PQ=10.
 Why are Manhole Covers Round? [05/09/2000]

Why are most manhole covers round? Why aren't manhole covers on the
streets squares or rectangles?
 Why a Square Maximizes Area/Perimeter [07/24/2002]

Is it possible to make a rectangle with a perimeter of 16 feet and an
area greater than 16 square feet?
 Why Do the Angles of a Triangle Add to 180 Degrees? [4/17/1996]

We were wondering why all the angles in a triangle add up to 180 degrees.
 Why do the Midpoints of Quadrilaterals Make a Parallelogram? [2/7/1996]

Why is it that if you join the midpoints of any quadrilateral you always
get a parallelogram?
 Why There Is No SSA Congruence Postulate or Theorem [03/29/2005]

In the correspondence of two triangles, if SSA = SSA, are the
triangles congruent?
 Will the Tree Hit the House? [05/18/1999]

A tree is leaning at 70 degrees, our house is 66 1/2 feet away, and the
angle from our house to the top of the tree is 40 degrees...
 World War II Window Blackout [10/21/2001]

Mr. Brown had a square window 120cm x 120cm, but the only material he
could find was a sheet of plywood 160cm x 90cm; same area, different
shape. He drew some lines and cut out just two congruent shapes, which he
joined to make a square of the correct size. How did he do it?
 You Can't Trisect an Angle [7/16/1996]

Who proved you can't trisect an angle?
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