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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.
 Triangle Congruence: AAS and ASA [10/16/2003]

Why isn't AAS (Angle, Angle, Side) used to prove that two triangles
are congruent?
 Triangle Construction [09/09/2001]

Given a triangle ABC and point D somewhere on the triangle (not a
midpoint or vertex), construct a line that bisects the area.
 Triangle Construction Given an Angle, the Inradius, and the Semiperimeter [03/26/2002]

Given an angle, alpha, the inradius (r), and the semiperimeter (s), construct the triangle.
 Triangle Construction Given Medians [12/12/2001]

Given median lengths 5, 6, and 7, construct a triangle.
 Triangle Construction Given Two Angles and Semiperimeter [03/14/2002]

Given two angles, A and B, and the semiperimeter, construct the triangle.
 Triangle Geometry: Sides and Edges [6/2/1996]

If the angles of a triangle are equal, does it necessarily mean that the
sides are also equal?
 Triangle Inequality Theorem [03/09/2001]

The lengths of the sides of a nonisosceles triangle, in size order, are
5, x, and 15. What are all possible integral values of x?
 Triangle: Longest Side Opposite Greatest Angle [10/23/1999]

Prove that in any triangle, the greatest side is opposite the greatest
angle.
 Triangle Midpoints and Vertices [02/23/2003]

How do you figure out the vertices of a triangle algebraically by
using its three midpoints?
 Triangle Perimeter [07/20/1997]

How many triangles have sides whose lengths total 15 units?
 Triangle Proof [2/18/1995]

Maybe if two sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the longer side. I'm not sure how to say this in a proof.
 Triangle Proof: Parallel Sides and Proportionality [07/27/2004]

How do I prove that a line which cuts two sides of a triangle
proportionately is parallel to the third side?
 Triangle Proof: r + r1 + r2 = CD [04/20/2001]

Let CD be an altitude of triangle ABC, and assume that angle C = 90
degrees. Let r1 and r2 be the inradii of triangle CAD and triangle CBD,
respectively, and show that r+r1+r2=CD, where r is the inradius of
triangle ABC.
 Triangle Proofs in General [11/19/2001]

Mapping out a general method for proceeding with proofs.
 Triangle Proof with Contradiction [02/21/2004]

Let D, E lie internally on side BC of triangle ABC and consider the
following conditions:
1) angle BAD = angle DAE = angle EAC
2) BD = DE = EC
Prove that, whatever the shape of triangle ABC, 1) and 2) cannot both
be true, that is, if either is true, then the other is false.
 Triangle Proportions: A Diagram [05/06/2003]

A cone has a circular base radius 1, and vertex of height 3 directly
above the center of the circle. A cube has four vertices in the base
and four on the sloping sides. What is the length of a side of the
cube?
 Triangles: Angle Sums [05/15/2002]

Can you draw a triangle in which the sum of any two angles  no
matter which two you pick  is always less than 120 degrees?
 Triangles in a Polygon [06/14/1997]

A regular 18sided polygon is inscribed in a circle and triangles are
formed by joining any three of the eighteen vertices. How many obtuse
triangles are there?
 Triangle's Medians Make Smaller Triangles with Equal Area [04/15/1999]

Proving that the six triangles constructed from the three medians of any
triangle have the same area.
 A Triangle Vertex Bisection and Its Trio of New Lengths [06/08/2012]

A trigonometry student struggles to express where the bisector of a triangle vertex
intersects the side opposite it; and to describe the bisector's length in terms of the
triangle's side lengths and angle measures. Doctor Peterson unpacks formulas for
both, along the way invoking the Law of Cosines — and another doctor's prior
work.
 Triangle Vertices But Not Sides [02/22/2003]

If P is a regular ngon, what is the number of triangles whose
vertices are the vertices of P but whose sides are NOT the sides of P?
 A Triangle with Three Right Angles [12/01/1999]

How can you make a triangle with three right angles?
 Triangular Garden [03/18/1997]

Find the length of a fence that runs from the right angle to the
hypotenuse and separates the garden into two parts of equal perimeter.
 Trisected Hypotenuse of a Triangle [12/20/1998]

In right triangle ABC, with C as the right angle... what is the length of
AB (the hypotenuse)?
 Trisecting an Angle and the Opposite Side in a Triangle [09/03/2008]

Prove that it is impossible to have a triangle in which the
trisectors of an angle also trisect the opposite side.
 Truncating a Square to Get an Octagon [10/13/2003]

I want to make an octagon by cutting the corners off of a square.
Where do I make the cuts?
 Twenty Quadrilaterals from Nine Dots [04/04/1999]

How can you get 20 quadrilaterals from 9 dots?
 TwoColumn Proof About Kites [11/09/1999]

Can you help me understand a proof about perpendicular lines and
congruent triangles in a kite?
 Two Column Proof of a Theorem [08/12/1998]

Write a twocolumn proof and give numbered statements with reasons....
 Two Questions on Geometric Harmonics [11/24/2005]

Two circles intersect each other at B and C. Their common tangent
touches them at P and Q. A circle is drawn through B and C cutting PQ
at L and M. Prove that {PQ:LM} is harmonic.
 TwoSided Polygon? [12/01/2003]

My 5th grade math teacher said that we had to draw a polygon using two
straight lines. Is this possible?
 Understanding Bearings in Directional Problems [01/14/2004]

A boat sails 10km from a harbor H on a bearing of S30 degree E. It
then sails 15 km on a bearing of N20 degree E. How far is the boat
from H? What is the bearing from H?
 Understanding Rectangle Area and Perimeter [11/08/2002]

True or false: if the perimeter of a rectangle increases, the
rectangle's area always also increases.
 Uniquely Determining a Polygon [02/05/2001]

Is it true that if you know the side order, side lengths, and area of a
polygon, as well as whether each of its angles is obtuse or acute, you
have uniquely determined it?
 Using Midpoints to Determine Vertices [09/04/2002]

The midpoints of the sides of a triangle have coordinates G(3,1),
H (1,2) and J (1,3). Determine the coordinates of the vertices
of the triangle.
 Using the Incenter [05/06/2003]

I need to construct a triangle to fit inside a triangle.
 Vectors of Parallelograms and Octagons [07/28/1998]

ABCDEFGH is a regular octagon and AB = p and BC = q. Express AH in terms
of p and q...
 Venn Diagram to Classify Quadrilaterals [01/02/2003]

I am looking for a Venn diagram that will accurately display the
relation among trapezoids, parallelograms, kites, rhombi, rectangles,
and squares.
 What Does a Myriagon Look Like? [10/30/2002]

I am looking for a picture of a myriagon.
 What does Angle ABC Equal? [3/5/1995]

A triangle, ABC, is obtuse angled at C. The bisectors of the exterior
angles at A and B meet BC and AC produced at D and E respectively. If
AB=AD=BE, then what does angle ABC equal?
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