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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.
 Perimeter of an Inscribed Regular Polygon [12/10/1998]

What is the formula for the perimeter of a regular polygon inscribed
inside a circle?
 Perimeter of a Right Triangle [08/14/2001]

What is the perimeter of a right triangle with hypotenuse 65 that can be
circumscribed about a circle with radius 12?
 Perimeter of a Strange Figure [03/23/2002]

I don't understand how to find the area or perimeter of a shape that
looks like a rectangle with a small triangle to the left on top...
 Perimeter of Octagon [04/02/1997]

What is the perimeter of a an octagonal garden with a diameter of six
feet?
 Pi and Polygons [03/14/1999]

Derive a formula to find the angle of an nsided polygon with x sides.
 Pick's and Euler's Theorems [05/06/1999]

What is Pick's theorem and how can it be linked with Euler's theorem?
 Pick's Formula [05/22/1997]

What is Pick's Formula?
 Pick's Theorem [9/4/1996]

Could you explain Pick's Theorem?
 Picture Frame, Triangle Measurements [5/20/1996]

My teacher gave us ten questions to answer and I could do all except two:
1) A framed rectangular picture is 35cm long and 25cm wide... 2) The base
of a triangle is 9cm more than the perpendicular height...
 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...
 Pixels in a Triangle [08/02/1999]

How can I find the number of pixels inside a triangle?
 Placing Coins That Touch [8/7/1996]

How many 20cent coins can you put around a 20cent coin so that all of
them touch?
 A Point Inside a Square [09/18/2003]

Point P lies inside square ABCD such that P's distance from A is 1,
P's distance from B is 4 and P's distance from C is 5. What is the
area of the square?
 Point Inside or Outside Triangle? [08/02/2001]

I have coordinates of three vertices of the triangle and coordinates of
the point.
 A Point in the Triangle [02/12/1999]

Finding the point P in a plane of triangle ABC, where PA + PB +PC is
minimum.
 Point within a Triangle [05/29/2003]

I have the coordinates of the three corners of a equilateral triangle
ABC. How can I decide whether an arbitrary point (X,Y) lies in the
plane of the triangle?
 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 Algorithms [05/10/2001]

Given a polygon as a set of points (X, Y) and a database table with X and
Y columns, select all records/points from the table that are inside the
polygon or belong to its border.
 Polygon Diagrams [05/11/2003]

I would like to see pictures of polygons with 11, 12, 13, 14, and 15
sides.
 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 Triangles [03/09/1999]

Prove that after splitting a regular npolygon into n triangles, the
isosceles triangles have greater area than the scalene triangles.
 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?
 A Practical Use for the Orthocenter [03/07/2001]

Does the orthocenter of a triangle have any practical uses?
 Probability in the Infinite Plane [03/29/2003]

Three randomly drawn lines intersect so as to form a triangle on an
infinite plane. What is the probability that a randomly selected point
will fall inside that triangle?
 Probability of Making Triangle with Three Stick Pieces [02/24/2007]

Take a stick of unit length and break it into two pieces, choosing the
break point at random. Now break the longer of the two pieces at a
random point. What is the probability that the three pieces can be
used to form a triangle?
 Proof by Contradiction [09/25/1997]

Prove that no isoceles right triangle exists which has all three sides
integers.
 Proof: Median of a Trapezoid Theorem [03/24/2001]

Prove that the median of a trapezoid is: 1) parallel to its bases; 2)
length = 1/2 the sum of the bases.
 Proof of Congruency [10/13/1996]

Line PR bisects angles QPS and QRS; prove that segments RQ and RS are
congruent.
 Proof of Hero's formula [09/08/1997]

Could you tell me where to find a proof of Hero's formula or help on how
to derive it?
 Proof of Morley's Theorem [08/09/2000]

How can I prove Morley's theorem (if every angle in a triangle is
trisected, each pair of trisectors meets in a point, and all three points
form the vertices of an equilateral triangle)?
 Proof of Pappus' Theorem [04/02/2001]

How can I prove Pappus' theorem of colinearity with the help of Menelaus'
theory?
 Proof of Pythagorean Theorem: Pythagoras' Reasoning [02/23/1998]

I would like to know how Pythagoras reasoned his theorem.
 Proof of the Feuerbach Theorem [03/14/2000]

Please submit the proof of the Feuerbach theorem (the ninepoint circle
is tangent to the incircle and the circumcircle of a triangle.)
 Proof of the Parallelogram Law [08/07/1999]

How do you prove the parallelogram law geometrically, without using
vectors?
 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?
 Proof Using Coordinate Geometry [06/08/2001]

In equilateral triangle ABC, a segment is drawn from point A to the side
BC at a point (D)... prove that angle BFC (or EFC) is a right angle.
 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 Triangle of Sides with Length... [8/1/1996]

Let a, b and c be the lengths of the sides of a triangle. Prove that the
square root of (a+bc) plus the square root of (b+ca) plus the square
root of (c+ab) is equal to or less than the sum of the square roots of
a, b and c. Determine when equality occurs.
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