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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.

Irregularly Inscribing a Circle ... of What Radius? [12/24/2011]
A student struggles to determine the radius of a circle given the sidelengths of an inscribed irregular polygon. First, Doctor Greenie offers a numerical approach; then, Doctor Floor follows up with the desired analytical method, applying Ptolemy's theorem and the rational root theorem to a key insight: the radius of the circumcircle remains invariant under a re-ordering of the polygon's sidelengths.

Is a Circle a Polygon? [03/07/1999]
A circle is not a polygon.

Is an Equilateral Triangle Also Isosceles? [02/19/2008]
Can equilateral triangles also be classified as isosceles? In other words, does an isosceles triangle have exactly two equal sides or at least two equal sides?

Is it Possible to Prove that... [10/28/1997]
... if the hypotenuse of a right angle triangle is divisible by 4, the legs are also divisible by 4?

Is Kite the True Name? [03/29/2002]
Is kite the true math name for this shape, or is there another?

Isosceles Trapezoid [6/23/1996]
Bases AB and CD of an isosceles trapezoid ABCD are 12 units apart...

Isosceles Trapezoid Proof [01/18/2002]
Given: ABCD is an isosceles trapezoid with bases BC and AD. Prove: ABCD is an isosceles trapzoid.

Isosceles Triangle - Angles [11/06/1996]
Given that one base angle of an isosceles triangle is 39 degrees, find the measure of the other two angles in the triangle.

Isosceles Triangle Maximizes Area? [09/11/2003]
How can you show that among all triangles having a specified base and a specified perimeter, the isosceles triangle on that base has the largest area?

Isosceles Triangle Proof [05/14/2006]
Given triangle ABC, with D on BC and AD bisecting angle A. The center of the circle circumscribing ABC is the same point as the center of the circle inscribed in ADC. Prove that ABC is a isosceles triangle.

Isosceles Triangles [2/8/1996]
A student asks how to find angle B of a given isosceles triangle.

Is This a Square? [01/30/2001]
Given four points on a graph, what can I do to verify this is a square?

Kitchen Tabletop [11/21/2001]
I need to determine the correct pivot point...

A Ladder Puzzle [10/20/2000]
A 10-meter ladder is leaning against a wall just touching the corner of a 3-meter cube placed flat against the wall. At what height does the end of the ladder touch the wall?

Largest Triangle in a Square [10/31/1998]
If the area of a square is 1, what is the largest area of a triangle constructed inside the square? How would you prove it?

Lattice Points in a Rectangle [06/04/1999]
How can I prove that in any rectangle centered at (0,0) with an area greater than 4, you can find lattice points other than (0,0)?

Lattice Points on Hypotenuse [10/01/2001]
What is the number of lattice points on the hypotenuse of a right triangle?

The Law of Margins [9/2/1996]
How do I figure out the margins of my mat using the Golden Ratio?

Learning to Read Proofs [10/31/2003]
How do you know what step comes next in a proof?

Least Perimeter [10/13/2002]
Finding a formula for least perimeter of a square or rectangle.

Left-Sided Rhombuses in a Larger Rhombus [05/22/2000]
How many left-sided, right-sided, and vertical rhombuses can be found in a larger NxN rhombus?

Leg of a Triangle [04/02/2002]
I need to know where the name "leg" of a triangle comes from, or what its origin is.

Length of a Triangle's Sides [1/23/1995]
I have a triangle problem for you to solve: The lengths of the three sides of a triangle could be...

Length of the Diagonals of a Parallelogram [05/22/2000]
A parallelogram has a 70-degree angle and sides 6cm and 10cm long. How long are its diagonals?

Limited Area, Unlimited Perimeter [11/27/1997]
What is the figure?

Limit of Area [03/01/1998]
Limit approached by area of a square when its sides are repeatedly divided into three congruent parts and squares are constructed outwardly on the middle parts.

Linear Systems of Equations in Two Variables [06/18/1999]
How can I find the length of AE, EB and DC, given that parallelogram ABCD has a perimeter of 50, trapezoid AECD has a perimeter of 39, and AE = EC?

Line Dividing a Plane [05/11/2001]
Given a square (graphed on the Cartesian coordinate system) and a point in the square, draw a line through the point that will divide the square into two regions: one the smallest area possible, the other the largest possible.

Lines Intersecting within a Polygon [10/24/1996]
Given an n-sided regular polygon with all vertices connected to each other by straight line segments, how do you determine the number of intersection points within the polygon?

Lines of Symmetry [01/29/2001]
How do you find the number of lines of symmetry there are in a polygon?

Lines of Symmetry in Regular Polygons [03/13/2001]
Is there a formula for finding all the lines of reflectional symmetry in regular polygons?

Locus [05/03/1999]
What is a locus?

Logarithms and the Area of a Triangle [6/3/1996]
Is is true that if A is the area of a triangle, then....log(A) = ...?

Longest Ladder [11/30/2001]
Two hallways, one 8 ft. wide and other 4 ft. wide, meet to form a right angle. What is the longest ladder that can go around the corner where the hallways meet?

Ludolph van Ceulen and Pi [11/02/1998]
How did Ludolph van Ceulen estimate pi by inscribing and circumscribing a circle with squares?

Magic Triangle Puzzle [07/26/2002]
Where did the white square come from?

Making a Pool Tarp [9/27/1995]
I'm trying to construct a pool frame out of pvc that will be placed over a pool. We already have the pool tarp, but we need to build something that will shed water so it has to have a slope. PVC only comes in 90 degree and 45 degree angles and straight sections. How do I figure out the maximum height the frame can stick straight up in the air to utilize the tarp?

Math and Sports [02/26/1997]
Can you give me information on how math relates to sports?

Maximize Area of Trapezoid [07/28/2003]
Given an isosceles trapezoid with three of its sides of length 10 cm, find the fourth side so that the area is maximized.

Maximizing Irregular Polygon Area: Which Circle? [05/01/2011]
How do you determine the radius of the circle that maximizes the area of an irregular n-gon circumscribed on it? With the Pari computer algebra system, Doctor Vogler approaches the question using numerical techniques such as Newton's Method and a binary search, which suggests that no closed-form expression exists.

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