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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. Triangle Area Proofs [01/23/2002] An analytic proof. Triangle Centers at Lattice Points [09/03/2002] Is there a triangle that can be plotted on a rectangular grid so that all of its vertices and all four centers are lattice points? If so, what are the coordinates of the vertices? 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 semi-perimeter (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 non-isosceles 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 18-sided 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 n-gon, 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? Two-Column 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 two-column 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. Two-Sided 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. Page: []

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