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 TOPICS This page:   triangles/polygons    Search   Dr. Math See also the Dr. Math FAQ:   geometric formulas and   naming polygons   and polyhedra and   Pythagorean theorem Internet Library:   triangles/polygons HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry 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. Constructing a Segment [09/26/1999] Given a 1" segment and a 2.5" segment, how can you find a segment of length sqrt(2.5)" using only a compass and a straightedge? Constructing a Square [12/25/1998] Given any four points, construct a square such that each side or extension passes through one point. Constructing a Triangle [08/20/1999] How can you construct a triangle with 3 different-size segments? Constructing a Triangle Given the Medians [01/01/2001] How can I construct a triangle ABC given AM, BN, and CP, the respective medians from the vertices A, B, and C? Constructing Polygons [06/03/1998] How do you construct a regular pentagon and a regular decagon? Can you construct a regular n-gon? Constructing the Orthocenter [01/27/1999] How do you construct the orthocenter of a triangle? Construct Polygon Given One Side [12/03/2001] How can you construct a polygon, given one side? Converse of the Pythagorean Theorem [02/14/2003] What is the converse of the Pythagorean theorem? Cosine Addition Formula [12/13/1997] How can you prove the addition formula for cosine by using right triangles? Counting Collinear Sides [04/12/2013] A student wonders how to count the sides of a polygon that has degenerate vertices. Citing Wikipedia and MathWorld, Doctor Peterson teases out the various conventions. Counting Diagonals [03/14/1998] How many diagonals can be drawn for a polygon with n sides? Counting Intersections of Diagonals in Polygons [03/08/2000] Can you help me find an equation for the maximum number of intersections of the diagonals in a polygon? Counting Rectangles Cut By a Diagonal [06/15/1999] How can we find an equation for the number of unit squares that are cut by a line going from corner to corner on a rectangle? Counting Sides by Counting Diagonals [06/04/2002] How can I find the number of sides in a polygon, given the number of diagonals? Covering Paper using Index Cards [10/24/2001] What is the maximum area of an 8"x13" sheet of paper that you can cover by using seven 3"x5" standard index cards? Cross-Cornering a Shape to Make it Square [12/19/2002] We lay out a building that is 30' x 40' and cross-corner it to see if it is 'square,' but there is a 6' difference. What is the equation to find how far to move one side to make the shape 'square'? Curious Property of a Regular Heptagon [04/06/2001] How can I prove that in a regular heptagon ABCDEFG, (1/AB)=(1/AC)+(1/ AD)? Cutting a Circle out of a Square [2/14/1996] What is the area (to the nearest square centimeter) of the largest circle that can be cut from a square piece of sheet metal 73cm. on each side? Explain how you determined this. Cutting a Square into Five Equal Pieces [07/12/1999] How can you divide a square cake into five equal parts, cutting through the center point? Cutting a Triangle into Two Congruent Triangles [10/06/1998] How do you cut a triangle into two congruent equilateral triangles with the minimum number of cuts? Cutting Carpet [9/9/1996] Two pieces of carpet are to be used to cover a floor. You are allowed to make just one cut in one of the two pieces... Cyclic Quadrilateral [05/22/2000] For an isoscles trapezium ABCD with AB paralled to DC and AB less than CD, how can we prove that ABCD is a cyclic quadrilateral? Cyclic Quadrilaterals [8/30/1996] A cyclic quadrilateral touches a circle at each vertex. What angles do these points make with the centre of the circle? Cyclic Trapezoid [01/17/2002] PQ is a diameter; AB is a chord parallel to PQ. If PQ=50cm and AB= 14cm, find PB. Defining Exterior Angles of Polygons [06/24/2004] My math teacher says the sum of the exterior angles of a triangle is 900 degrees (360*3 - 180). I think that the sum is 360 degrees. Who is correct? Definition of Opposite Sides [01/18/2001] What is the formal definition of 'opposite sides' of a polygon? Does a regular pentagon have opposite sides? Does a concave polygon have opposite sides? How can we define it consistent with our intuition? Degenerate/Nondegenerate Figure [10/27/2001] We need to know what a nondegenerate circle is. (We're trying to decide whether this is a model of incidence geometry, but don't know the definition.) Degenerate Triangle [09/03/2003] Isn't a degenerate triangle really just a line segment? De Longchamp's Point [09/21/2000] What is De Longchamp's point, and how is it used? Derivation of Law of Sines and Cosines [11/02/1997] How do you derive the law of sines and the law of cosines? Derivations of Heron's Formula [11/24/1998] How is Heron's formula (Hero's formula) derived? Derivations of Pi and a Polygon of Degree n [3/4/1995] I am curious about the derivation of pi and the formula for deriving a polygon of degree n. Can you help? Deriving the Distance Formula from the Pythagorean Theorem [03/23/2003] How does one derive the distance formula from the Pythagorean theorem? Deriving the Law of Cosines [04/01/1998] Will the Pythagorean Theorem work with a non-right triangle? Deriving Trilinear Coordinates [05/18/1999] How do you derive the trilinear coordinates of the orthocenter of a triangle? Desargues' Theorem and SSASS [12/15/1998] What is the main theory behind Desargues' Theorem? Also, is SSASS a valid method for proving two quadrilaterals are congruent? Determinants and the Area of a Triangle [12/14/1998] Given a triangle with vertices (A,B), (C,D), and (E,F), how do you find the area in determinant form? Determine if Point is in Rectangle [5/29/1996] What formula will allow me to determine whether a specified point lies within a polygon (rectangle - 4 points)? Determining Area of a Lot of Land [08/20/2003] We are trying to figure out the square footage for a lot that I own. Determining If a Given Point Lies inside a Polygon [12/27/2005] I have a finite number of points that constitute a polygon, and a point p(x,y). I want to know if point p lies inside the polygon. Page: []

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