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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. 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 2001-gon [05/29/2002] What is the largest possible number of acute angles a 2001-gon 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. Mid-segment Theorem [02/02/1999] Can you help me prove the Mid-Segment 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? Nine-Sided Polygon [06/11/1997] Can you construct a regular 9-sided polygon inside a circle using only a compass and straight-edge? Nonagon or Enneagon? [02/06/2003] Is 'enneagon' really the correct name for a 9-sided polygon? Non-Congruent Triangles [12/12/2001] Construct and prove that there can be two non-congruent 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 12-foot 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 Two-sided 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 origami-like 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. Page: []

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