What is Triangle: Definition and 1000 Discussions

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted



△
A
B
C


{\displaystyle \triangle ABC}
.In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted.

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  1. F

    Proof: circumference of circle inscribed in a triangle < perimeter of the triangle

    Homework Statement A circle is inscribed in a triangleHere is a picture Picture of circle inscribed in triangle, not necessarily to scaleWhich is larger: the circumference of the circle, or the perimeter of the triangle? Homework EquationsC=∏D (D=diameter of the circle, C=circumference of...
  2. W

    MHB Calculating the Height of an Isosceles Triangle Using Coordinates and Equations

    A (51) D E (42) C (56) H (56) B Isosceles triangle ABC, AB = AC, base BC = 112. D is on AC: line BD crosses height line AH at...
  3. E

    MHB Can a Triangle Have Angles of 55°, 65°, 70°; 53°, 64°, 73°; 80°, 105°, 5°?

    thanks.. an explanation on how to do it will help!1.Can a triangle have angles equal to a. 55°, 65°, 70° b. 53°, 64°, 73° c. 80°, 105°, 5° 2. In (triangle)△DEF, <D, <E and <F -44° (deg), Find <D and <E
  4. Feodalherren

    Triangle inside circle, find area of circle.

    Homework Statement An equilateral triangle of side x is is inscribed in a circle. Express the area of the circle as a function of x. Homework Equations Anything non-trig. I suspect it's got something to do with the Pythagorean theorem. The Attempt at a Solution I tried getting the...
  5. H

    MHB Basic trig, solving side of triangle

    Here is what I got so far: But the solution 15.7875 MPH is incorrect so undoubtedly my angle would come out incorrect too. Where have I gone wrong?
  6. DeusAbscondus

    MHB Discovering the Truth Behind the Side Ratios of a 30:40:90 Triangle

    (Plse bear with me: until i learn how to fly this thing, / must stand for radical) If the side ratio for a 30:40:90 deg right triangle are 1 : /3 : 2 then, is the following true: one may multiply this ratio by 1,2,3 or 5,6,7,8,9 or 10 and the pythagorean identity obtains but NOT by 4 If so...
  7. W

    Probability obtuse triangle - simple one

    Homework Statement The two sides lengths of a triangle is exponentially distributed. (not so important for my question) The angle between the sides is uniformly distributed [0,2∏] c) explain why the probability to get obtuse triangle is greater then 0.5 The Attempt at a Solution...
  8. Y

    Finding equation of plane containing triangle

    Homework Statement B(-6,-7,-3) C(2,7,3) D(-4,-1,-11) Find the equations of the plane containing the triangle BCD. The attempt at a solution I've gotten to the end and got an equation, but the normal vector it has is just making me really paranoid. Vector BC = [2+6, 7+7, 3+3] =...
  9. D

    Centroid of a right angle triangle

    Hi i have a right angle tringle, base=1200m and h=400. I have trouble understanding on how to determine the centroid i know one side will be 2/3*x and another side would be 1/3*y. But i don't understand how to write it out. A friend said its 1/3*1200*400*2/3*1200, but i have no idea and...
  10. B

    An angle - why an angle is the ratio of two sides of a triangle?

    An angle -- why an angle is the ratio of two sides of a triangle? Perhaps I should have already learned this, but I just can't seem to grasp why an angle is the ratio of two sides of a triangle, or the length of a circular arc by its radius.Why is this so?
  11. W

    Triangle geometry find a side length

    Homework Statement In triangle ABC, the median from C meets AB at D. Through M, the midpoint of CD, line AM is drawn meeting CB at P. If CP=4, find CB. Homework Equations The Attempt at a Solution I constructed this drawing on GSP and found CB to be 12. I'm trying to show...
  12. J

    Baby Rudin Proof of Theorem 1.33 (e) - Triangle Inequality

    Hi everyone, I have a question on Rudin's proof of Theorem 1.33 part e. Here he prove the following statement: The absolute value of z+w is equal or smaller than the absolute value of z plus the absolute value of w -Yes, is the triangle inequality, where z and w are both complex numbers-...
  13. A

    Triangle Inequalities Relationship

    I know the following |x|-|y| \leq |x+y| \leq |x| + |y| where does |x-y| fit in the above equation?
  14. H

    Irodov Equilateral Triangle Problem

    Homework Statement Hello, so I'm going to be a freshman physics major next year, and over the summer I'm trying to improve my problem solving skills. I've started going through Irodov's problems in general physics, and I have a question about two different solutions to one of the problems...
  15. P

    Prove Triangle ABC has Angle BAC = 72 Degrees

    Hey guys, This is NOT homework. I remember solving this question many years ago (at least 10 years ago). I am trying to recall the solution again and am just not able to. The question is - In a triangle ABC, AD is the angle bisector of angle BAC. AB = CD. Prove that angle BAC = 72 degrees...
  16. W

    Finding the unknown points of a second triangle

    Homework Statement Triangle A has three points a(2,3)b(0,0)c(2,0) and its center is (2/3,1). Find the other three points of Triangle B with a center of (4/3,3). Homework Equations Center of a triangle: x = ax+bx+cx /3 y = ay+by+cy / 3 Magnitude = <a,b> , √(a^2+b^2) The Attempt at...
  17. M

    Volume of cross sections using isosceles right triangle

    Homework Statement The area is bounded by the equation y=x^2, x-axis and the line x=3 and is perpendicular to the x axis Homework Equations A=1/2bh Height=Base The Attempt at a Solution A=1/2B^2 V=1/2B^2 from 0 to 3 V=1/2 B^3/3 from 0 to 3 V=B^3/6 from 0 to 3 V=27/6 please...
  18. R

    Triangle Integral Formula: Uncovering the Truth Behind b3/6

    Homework Statement the formula of a triangle is b2/2, so the integral should be b3/6, right? Well, that can't be right. Because if the base of the triangle is 4, it's area will not add up to 8. What am I doing wrong?
  19. X

    Solving Similar Triangles Homework

    Homework Statement see attachment Homework Equations The Attempt at a Solution No idea how to do this. Tried extending the 10 thus getting a big triangle of (10+x)^2+y^2=400. But then again no idea what x and y is. This is wrong. Any help would be appreciated.
  20. L

    Convert a Quadrangle to a Triangle

    Hi all ! I got stuck in establising an method to Convert a Quadrangle mesh to a Triangle mesh (CFD). I have a mesh file (.dat) which have information: Number of Element - Node 1 - Node 2 - Node 3 - Node 4 1 1 2...
  21. A

    Bermuda Triangle: Unsolved Mysteries & Gravitational Forces

    What is Bermuda Triangle? Is gravitational Forces exist there or not?
  22. A

    Finding xy coordinates of obtuse and acute triangle

    This might seem easy, but I am sort of rusty on the math since i haven't taken a math course in a while. Homework Statement A 2 meter long bar lies in the xy plane with one end at the origin. find position at the xy plane of the other? end point of the bar if the angle the bar makes with...
  23. F

    Supression factor for triangle diagrams

    I'm pretty shaky with my understanding of much beyond simple tree-level calculations. When people talk about triangle diagrams, they sometimes say one will get a 'supression factor' of xxx. For example, in the consider the triangle diagram for H\rightarrow\gamma\gamma with Ws running around...
  24. L

    Area moment of inertia of inverted triangle?

    Homework Statement A inverted isosceles triangle gate with height a=3ft and base b=2ft is 6ft under the water (top of the inverted triangle). Find the Force on the gate and hp (the depth of the) center of pressure. Homework Equations hc= depth to gate + depth to centroid= 6+(1/3)•3= 6+1 =...
  25. G

    CHSH and the triangle inequality

    Hello everybody, I've been trying to understand the CHSH proof as it is listed on Wikipedia: http://en.wikipedia.org/wiki/CHSH_inequality I got to this without any problem: E(a, b) - E(a, b^\prime) = \int \underline {A}(a, \lambda)\underline {B}(b, \lambda)[1 \pm \underline {A}(a^\prime...
  26. W

    MHB Find Side AB of Triangle ABC Given M, N, and C

    B 15 A 9 M 11 N 5 C Triangle ABC, BC = 15, AC = 25. M and N on AC, such that AM = 9, MN = 11 and CN = 5. Angle ABM = angle CBN. Calculate side AB.
  27. T

    Proving Ceva's Theorem with Triangle PQR

    I have tried but still cannot get it. Simple geometry question. Tangents to the inscribed circle of triangle PQR are parallel to [QR], [RP] and [PQ] respectively and they touch the circle at A, B and C. Prove that [PA], [QB] and [RC] are concurrent relevant formula: Ceva's theorm (Any...
  28. 3

    Triangle length and largest angle

    Homework Statement A triangle has sides of length (n2+n+1), (2n+1) and (n2-1), where n > 1. (a) Explain why the side (n2+n+1) must be the longest side of the triangle (b) Show that the largest angle, θ , of the triangle is 120º. Homework Equations In a triangle of sides a, b...
  29. H

    MHB Finding the equation of vertex of right angle triangle

    Points (6,0) and (O,8) are the endpoints of the hypotenuse of a right-angled triangle, whose other vertex is at (x,y). What equation relates x and y?Attempt at solution: So What I am thinking is that the line will be perpendicular to the line with end points 6,0 and 0,8. So The gradient of...
  30. H

    Finding the equation of vertex of right angle triangle

    Points (6,0) and (O,8) are the endpoints of the hypotenuse of a right-angled triangle, whose other vertex is at (x,y). What equation relates x and y?Attempt at solution: So What I am thinking is that the line will be perpendicular to the line with end points 6,0 and 0,8. So The gradient of...
  31. G

    Solving Right Triangle question

    Homework Statement I am having trouble with right triangles. I understand how to use the formulas, however I don't know which angle is appropriate when using the formulas. For example, in this picture: http://imgur.com/C2lxg . There was a problem in my book that had a triangle like this. The...
  32. S

    Calculating Routes on a Grid: Using Combinations and Pascal's Triangle

    1. The streets of a city are laid out in a rectangular gird, as shown below a) Use combinations to find the number of routes through the grid that lead from point A to point B by only traveling north or east. Show your calculations b) How many of these routes pass through intersections...
  33. M

    Triangle plane surface 2m base and 3 height

    Hello .. This is a question with answer , From where " 1 " in the solution ? http://store1.up-00.com/Mar12/yd170715.jpg
  34. mishima

    Moment of Inertia in Equilateral Triangle

    The problem is to find the moment of inertia for a solid equilateral triangle about an axis at the triangle's vertex which is perpendicular to the plane of the triangle. Mass is given as M. I was wanting to treat it like 3 point masses at each vertex with 1/3 mass. Then I could use the sum...
  35. P

    Volume of a solid with equilateral triangle cross-sections

    The base of a solid is the region bounded by the parabola x2 = 8y and the line y = 4 and each plane section perpendicular to the y-axis is an equilateral triangle. What is the volume of the solid?(Barron's Problem) so I solved for x since y must be used because the cross section is...
  36. T

    The distances of vertices of an equilateral triangle

    Homework Statement The distances from the vertices of an equilateral triangle to an interior point P are √a, √b, and √c respectively,where a, b, and c are positive integers. Find the minimum and the maximum values of the sum a + b + c if the side of a triangle is 13. Homework Equations the...
  37. V

    Intersection of vector and triangle side

    Homework Statement I have a triangle with given vertices ABC. Given a vector that starts from A and intersects side BC, how can I find the point of intersection, p? Thanks Homework Equations The Attempt at a Solution
  38. O

    Solve a Triangle using Trigonometry

    Homework Statement http://img23.imageshack.us/img23/9427/imageyakj.jpg AC+CB=24 The bisector = 8. Find angle DCB, i.e. x. Homework Equations The Law of sines, I think.The Attempt at a Solution
  39. C

    Help visualising this triangle

    Homework Statement I think this must be really easy but I am not getting a visual for this triangle description. Let ABC be a triangle with \UparrowOA=a and /UparrowOB=b and /UparrowOC = c Where O is the origin . Homework Equations The Attempt at a Solution How can I...
  40. O

    Finding Derivitive of a Triangle Area

    My answer to this question seems close to that of the book but I have only solved for +1/2 and not the -1/2. Can anyone help? Many thanks. Homework Statement Q. The area of a triangle is \frac{-4m^2 + 4m - 1}{m}. Find the value of m via differentiation. Homework Equations The...
  41. M

    Naming a triangle for a vectors question

    Homework Statement Triangle ABC has A (−1, 3,−3), B (2, 4, 6) and C (3, 0,−5). Use the scalar product to find the angle ACB. No pictures are given The Attempt at a Solution I have attempted the question by naming the triangle ABC with each angle opposite the line with the same...
  42. 4

    Charges on an equilateral triangle

    Homework Statement Charges Q, Q, and q lie on the corners of an equilateral triangle with sides of length a. Charge q lies on the top corner with Q and Q on the left and right corners. (a) What is the force on the charge q? (b) What must q be for E to be zero half-way up the altitudeat...
  43. M

    Electrostatic Forces of an Equilateral Triangle

    Homework Statement Three point charges are located at the corners of an equilateral triangle as in the figure below. calculate the net electric force on the 7-nc charge. Each sides are .5 m. (q1=7μc) (q2=2 μc) (q3= -4 μc) ___1 __/__\ 2/____\3 Homework...
  44. Math Amateur

    Area of a Triangle and Elliptic Curves - Birch and Swinnerton Dyer Conjecture

    In the book by Keith Devlin on the Millenium Problems - in Chapter 6 on the Birch and Swinnerton-Dyer Conjecture we find the following text: "It is a fairly straightforward piece of algebraic reasoning to show that there is a right triangle with rational sides having an area d if and only if...
  45. S

    Circle Inscribed in Triangle: Area Ratios with Inscribed Circle Tangents

    Homework Statement Consider a triangle ABC, where angle A = 60o. Let O be the inscribed circle of triangle ABC, as shown in the figure. Let D, E and F be the points at which circle O is tangent to the sides AB, BC and CA. And let G be the point of intersection of the line segment AE and the...
  46. C

    Calculating Triangle Area in 4-Space: Can Cross Products Be Used?

    Homework Statement Find the area of triangle with vertices (-2,-2,2,2), (0,0,1,-1), (-1,-2,1,1) Homework Equations The Attempt at a Solution The only way I know how to find the area of a triangle is by finding half the parallelogram. I.e. A = (1/2)||u x v|| But this requires cross...
  47. caffeinemachine

    MHB Ten segments. One can form a triangle.

    Each of ten segments has integer length and each one's length is greater than 1cm and less than 55cm. Prove that you can select three sides of a triangle among the segments.
  48. S

    Circulation over a triangle in R^3

    I have attached a file with all needed information including the function and path of integration. My work seems right to me, but the correct answer is a^2. Will someone please take a look and show me where my misstep is.
  49. T

    Forces on Equilateral triangle truss

    Hey Guys, My question involves finding all of the forces acting upon each member. It is known that each side of the triangle has a length of l. It is also known that the force is acting at the very top of the triangle in the x direction (to the right) labelled as F. Attempt: I found moments...
  50. J

    Proving the triangle inequality property of the distance between sets

    Proving the "triangle inequality" property of the distance between sets Here's the problem and how far I've gotten on it: If you are unfamiliar with that notation, S(A, B) = (A \ B) U (B \ A), which is the symmetric difference. And D(A, B) = m^*(S(A, B)), which is the outer measure of...
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