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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.
 Maximum Area of Inscribed Triangle [12/10/2001]

An isosceles triangle is inscribed in a circle of radius R. Find the
value of Theta that maximizes the area of the triangle.
 Maximum Number of Acute Angles in a 2001gon [05/29/2002]

What is the largest possible number of acute angles a 2001gon can
have if no two sides cross each other?
 Maximum Rectangle within a Quadrilateral [10/25/2001]

I need to extract from a quadrilateral the maximum area rectangle inside
it.
 Maximum Surface Area [07/03/2003]

Within a rectangle x by y, I wish to draw a shape that is no more than
x across in any direction, but which has the largest possible surface
area within the confines of the rectangle.
 Measures of Interior and Exterior Angles of Polygons [07/07/2005]

A question about star polygons leads to a discussion about calculating
interior and exterior angles of polygons.
 Measuring by Shadows [05/22/2001]

How can I measure a tree using its shadow and mine?
 Measuring the Height of a Building Using Shadows [05/24/2000]

What time of day is best to use a shadow to measure the height of a
building by using triangles?
 Median and Altitude Constructions [07/16/2003]

How to draw a median and an altitude from the three sides of a
triangle.
 Medians of a Triangle [02/16/1999]

Prove that the 3 medians of a triangle divide themselves up into a ratio
of 1:2.
 Medians of Triangles Proof [05/29/2000]

Prove that in any triangle, the sum of the medians is more than 3/4 of
its perimeter, but less than the whole perimeter.
 Menelaus's Theorem [01/25/1999]

A straight line intersects sides AB, BC and the extension of side AC of a
triangle ABC at points D, E and F respectively. Prove that the midpoints
of the line segments DC, AE and BF lies on a straight line.
 Midsegment Theorem [02/02/1999]

Can you help me prove the MidSegment Theorem?
 Minimal Distances to a Point in a Triangle [01/05/2001]

How can I prove that the smallest value of PA + PB + PC occurs when angle
APB = angle BPC = angle CPA = 120 degrees, for a triangle ABC and a point
P?
 Minimum Angle Proof [07/05/2001]

Label the point of intersection of the angle bisectors of triangle ABC as
Q. Let M be the midpoint of side BC. Given that MQ = QA, find the minimum
value of angle MQA.
 Miquel Circles [09/17/2003]

Given an acute triangle ABC, consider all equilateral triangles XYZ, where points A, B and C lie on segments XZ, XY, YZ. Prove that all centers of gravity of all these triangles XYZ lie on one circle.
 Mixtilinear Incircle Proof [12/11/2000]

In triangle ABC, AB = AC. A circle is tangent internally to the
circumcircle of triangle ABC and also to sides AB and AC at points P and
Q, respectively. How can I prove that the midpoint of the segment PQ is
the center of the mixtilinear incircle of triangle ABC?
 Nagel Point [04/15/2001]

What relation does the Nagel Point have to the incenter, centroid, and
Spieker point of a triangle?
 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 the Isosceles Triangle [09/23/1998]

How did the isosceles triangle receive its name?
 The Napoleon Point and More [09/04/1998]

How do you prove that the Napoleon point will always exist, given the
proper conditions? Is there a stronger theorem?
 Napoleon's Triangle [08/10/1999]

What is Napoleon's triangle?
 NineSided Polygon [06/11/1997]

Can you construct a regular 9sided polygon inside a circle using only a
compass and straightedge?
 Nonagon or Enneagon? [02/06/2003]

Is 'enneagon' really the correct name for a 9sided polygon?
 NonCongruent Triangles [12/12/2001]

Construct and prove that there can be two noncongruent triangles in
which five parts of one triangle are equal to five parts of another.
 Nonconvex Polygon Angle Measure [02/03/1999]

What is the formula to find the interior angle measurements of a
nonconvex polygon?
 Number of Lines of Symmetry in a Regular Polygon [03/12/1998]

In a regular polygon, is the number of lines of symmetry the same as the
number of lines or angles of that 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?
 Octagon Construction Using Compass Only [02/22/2002]

Construct the vertices of a regular octagon using just a compass. The
only thing you know about the octagon is the circumradius.
 Octagon Formula [07/30/1997]

If you're building an octagon on a 12foot radius, what is the length of
each side?
 Octagon Side Lengths [08/22/2001]

If I know that the dimension of an octagon from one side to the other is
8 feet, how can I find the lengths of a side?
 One and Twosided Polygons [12/07/1999]

Can you explain what a monogon and a digon are?
 Order of a 3D Triangle [08/29/2001]

If I visit the vertices of a 3D triangle in order going from a to b to c,
am I going clockwise or anticlockwise?
 Origami Equilateral Triangle [04/26/2001]

How can I create an equilateral triangle from a piece of paper using only
origamilike folds?
 Orthic Triangle [04/09/1999]

How do you find the angles of the triangle ABC, similar to triangle
A1B1C1, where AA1, BB1, and CC1 are the altitudes of triangle ABC?
 Overlapping right triangle problem [09/14/1997]

Given right triangles ABC and DCB with rt angles at B and C, triangle
ABC's hypotenuse 20 and triangle DCB's hypotenuse 30. The hypotenuses
intersect at point E, a distance of 10 from BC. Find the length of BC.
 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?
 Parallelogram Side Length [08/12/2003]

In a parallelogram ABCD, K is a point on AB such that angle DKC = 90
degrees and AD = AK. If AD = 10cm, find the length of AB.
 Pascal's Theorem [10/07/1998]

Can you explain Pascal's Theorem? How does it relate to conic sections?
 Pedan Trapezium [05/23/2000]

How can I prove that a isosceles trapezium whose parallel side lengths
are 7 and 4 respectively, and whose slant sides have length 6, is a Pedan
trapezium?
 Pentagon Area Using No Trig [05/14/2001]

Where I am stumped is finding the area of one of the five triangles.
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