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.

View More On Wikipedia.org
Recent contents Top users
  1. I

    Potential Difference Between Points on Dielectric Triangle

    Homework Statement A dielectric equilateral triangle of dielectric constant 30 is inserted into uniform horizontal electric field of 100,000 N/C. What is the potential difference between two points 3 cm apart on one of the sides? Homework Equations ΔV =∫E⋅dl E' =E/κ The Attempt at a...
  2. anemone

    MHB Triangle Challenge: Evaluate $\cos \angle B$

    In a triangle $ABC$ with side lengths $a,\,b$ and $c$, it's given that $17a^2+b^2+9c^2=2ab+24ac$. Evaluate $\cos \angle B$.
  3. M

    I Is the Sum of All Triangles Really Infinite? A Problem to Discuss

    Hi PF! A friend asked me to look at a problem, said it was on his mind. Rather than restate it here (since a picture helps) please check out the attachment. I drew a picture in tikZ and gave my attempt at a solution, but something in my gut feels the answer is infinite. I'd love to talk with...
  4. S

    Induced EMF in a Triangle: Determining EMF and External Force

    Homework Statement Magnetic Field B is going into the plane. Bar is moving to the right with velocity v. Neglect resistance of the conducting bar and all contacts. a.) Determine the induced emf in the circuit. b.) To maintain the uniform motion of the conductive bar, there must be an external...
  5. Albert1

    MHB Finding Angle C in Triangle ABC

    $\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\ find \,\, \angle C=?$
  6. I

    Velocity of Three Charges Released from Equilateral Triangle

    Homework Statement Three equal charges with charge q and mass m are placed into an equilateral triangle of side length L. Find the speed of each when they are infinitely far from one another. Homework Equations -ΔU =ΔK (since the electric force is conservative), U= 1/4πε Σq1q2 /r The...
  7. R

    Calculating Work to Move a Charge in an Equilateral Triangle

    Homework Statement two particles with charges 4e and -4e are fixed at the vertices of an equilateral triangle with sides of length a. If k=1/4 pi Ԑ what quantity of work is required to move a particle with a charge q from the other vertex to the center of the line joining the fixed charges...
  8. G

    Find Vector \overrightarrow{B_1B} for Triangle ABC

    Homework Statement Given points of a triangle: A(4,1,-2),B(2,0,0),C(-2,3,-5). Line p contains point B, is orthogonal to \overline{AC}, and is coplanar with ABC. Intersection of p and \overline{AC} is the point B_1. Find vector \overrightarrow{B_1B}. Homework Equations -Vector projection - Dot...
  9. karush

    MHB Area and angles of iso triangle given find sides

    Given an Isosceles triangle with the area of 100 with internal angles of $$40^o, 70^o,70^o$$ $A=\frac{1}{2}bh$ so $100=\frac{1}{2}\left(z\sin\left({70^O}\right)\right)\left(2z\cos\left({70^o}\right)\right)$ $z$ is length of one the equal sides At least started here
  10. anemone

    MHB Triangle Challenge: Proving Inequality of Sides

    Let $a\,b$ and $c$ be the sides of a triangle. Prove that \frac{a}{b+c-a}+\frac{b}{a+c-b}+\frac{c}{a+b-c}\ge 3.
  11. J

    Proving a parallelogram is a rhombus, given an Isosceles triangle

    I believe I could work this problem fine had the instructor not placed statements #3,4, and 6, as well as the reasons # 5 and 7. I can't seem to understand where he's using the transitive property in #5. If these steps weren't here I would assume, I'm only using substitution to prove that "RS"...
  12. MacLaddy

    Turbomachinery velocity triangle problem

    Homework Statement Air (assumed incompressible) flows across the rotor shown in the figure such that the magnitude of the absolute velocity increases from 15 m/s to 25 m/s. Measurements indicate that the absolute velocity at the inlet is in the direction shown. Determine the direction of the...
  13. X

    Phasor angular velocity for a triangle wave?

    What would the angular velocity for a phasor be for a triangle wave? I think it would vary sinusoidally but I can't find an expression
  14. Y

    How Sin(90° + θ) =sin θ of triangle P'OM'

    Hello everyone. I'm learning Trigonometry right now with myself and at current about how to find the trigonometric ratio of the angle (90° + θ) in terms of θ. I'm quite confused in the Figure. How sin(90° + θ) become equal to sin (90° - θ) of triangle P'OM'. I know that triangle P'OM' and POM...
  15. Albert1

    MHB Existence of the triangle

    Prove that there exists a triangle which can be cut into 205 congruent triangles.
  16. N

    Solving Triangle ABC: Finding Value of x

    Homework Statement In triabgle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120 degrees. Calculate the value of x? Homework Equations I used the cosine rule here The Attempt at a Solution As we have 2 sides and an angle I used the cosine rule - Am I correct? (2) means squared b(2)...
  17. Julian102

    Electric intensity at orthocenter of a triangle.

    Homework Statement At the vertices of a triangle there are + 5C, -7C, -3C of charge respectively. What is the electric intensity and direction at its orthocentre? Homework Equations Each side of the triangle is 1 mm in length. The Attempt at a Solution [/B] I failed to find the distance of...
  18. L

    MHB Formulas for Triangle Perimeter & Height

    Write the following formulas: a) The minimum perimeter of any triangle (abc) only known heights corresponding to the sides a and b. b) The maximum height and minimum corresponding to the side b of any triangle (abc) only known the value of its perimeter and height corresponding to the side a.
  19. L

    MHB Maxima and minima of a triangle

    Write the following formulas: a) The minimum perimeter of any triangle (abc) only known heights corresponding to the sides a and b. b) The maximum height and minimum corresponding to the side b of any triangle (abc) only known the value of its perimeter and height corresponding to the side a.
  20. L

    MHB Calculate the area of a triangle knowing its 3 heights

    Calculate the area of a triangle knowing its 3 heights ha = 3 m hb = 4 m hc = 5 m NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 10.03 m2 B) 10.04 m2 C) 10.05 m2 D) Imposible
  21. L

    MHB Calculate the area of a triangle knowing its perimeter and 2 heights

    Calculate the area of a triangle knowing its perimeter and 2 heights perimeter = 30 m ha = 8 m hb = 9 mNOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 41.29 m2 B) 42.93 m2 or 36.28 m2 C) 42.95 m2 or 36.29...
  22. L

    MHB Calculating Isosceles Triangle Side Length with Perimeter & Area

    That value has to have one side of a triangle to be isosceles knowing its perimeter and area. Area = 40 m2 Perimeter = 30m NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 13.33 m B) 19.18 m or 4.54 m C)...
  23. L

    MHB Calculate the sides of a triangle knowing its area, perimeter and angle A.

    Calculate the sides of a triangle knowing its area, perimeter and angle A. Area = 30 m2 Perimeter = 30m Angle A = 30º NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 6.09, 9.36 and 14.55 B) 7.40, 8.63 and...
  24. T

    Triangle formed by tangents to a parabola

    Homework Statement The triangle formed by the tangents to the parabola y2=4ax, at the ends of the latus rectum and the double ordinate through it's focus is: 1) equilateral 2) acute angles isosceles 3)right angled isosceles 4) dependent on value of a Homework Equations...
  25. D

    Determining the area of a triangle

    Homework Statement http://i.stack.imgur.com/KzCIl.png From the given picture the known quantities are: ##r = 7*3^{1/2} ## ##BC = 13 ## angle opposite to AC is ##120 ## degrees Homework Equations 3. The Attempt at a Solution [/B] I figured i could use a sine rule to get the side ##AC ##...
  26. D

    What is the area of a square drawn inside a triangle?

    Homework Statement Given the isosceles triangle whose sides are : c=10 b=13 find the are of a square drawn inside the triangle whose upper edges touch the b sides of the triangle. Homework Equations 3. The Attempt at a Solution [/B] I named the side of the square a. First i made two equations...
  27. S

    MHB Solve Proving 2 Triangles Cong. w/ Diam & Eq. Triangle (2-Col Proof)

    Not sure how to solve considering nothing is given as perpendicular or bisected. Is anyone aware on how to solve this problem? ~S.R.K.
  28. D

    Area of a triangle under a curve

    Homework Statement The tangent line of a curve y=e^(-x) intercepts the axises at points A and B. What is the maximum area of a triangle AOB considering O as the origin. Homework Equations Ar= xy/2 The Attempt at a Solution Derivative of this function is y'=-e^(-x) I took the formula of the...
  29. A

    Primitives triangle with smallest side an even number

    Homework Statement Prove that if a right triangle has all sides rational and primitives (co-primes), then one of the smaller side must be even number. Homework Equations For a right triangle (a,b,c) with c is the hypotenuse. $$a^2+b^2=c^2$$ The Attempt at a Solution In order to create a...
  30. B

    Find Lambda from this arbitrary triangle

    Folks, I am puzzled how one obtains equation 3.2.31 based on the schematic as attached! Can you help? Is there an online source I can refer to to learn how to obtain angles and magnitudes of complex schematics? Thanks
  31. M

    Why Use Logarithms to Solve Trig Problems?

    Hi, Can somebody please point me into a direction how to solve the attached trig problem? First step, where can I find such values for sin (alpha)?Thanks.
  32. J

    Refraction in Isosceles triangle [Uni Phys 2]

    Homework Statement Suppose the isosceles prism of the figure(http://imgur.com/EQiQSoO) has apex angle φ = 53.4° and index of refraction n = 1.41. (a) What is the smallest angle of incidence θ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of...
  33. B

    Triangle inequality implies nonnegative scalar multiple

    I'm not really sure if this is true, which is why I want your opinion. I have been trying to prove it, but it will help me a lot if someone can confirm this. Let ## v_{1}, v_{2} ... v_{n} ## be vectors in a complex inner product space ##V##. Suppose that ## | v_{1} + v_{2} +...+ v_{n}| =...
  34. anemone

    MHB Find the lengths of the sides of a triangle

    Find the lengths of the sides of a triangle with 14, 22 and 28 as the lengths of its altitude.
  35. C

    MHB Find the Sides of Triangle DEF: A Challenge!

    I found this question in my study guide triangle ABC is similar to triangle DEF. Triangle ABC has sides 4,6,8. Wich could be the corresponding sides of a triangle DEF? Indicate all that apply A) 1, 1.5, 2 B)1.5, 2.25, 3 C)6, 9, 12 D) 8, 12, 16 E)10, 15, 20 What I did was add the...
  36. V

    How Does an Equilateral Triangle Affect Electric Fields on Its Axis?

    Hi, I'm trying to solve this exercize : I/3 charges Q, positives, are at the corner of an equilateral triangle of centre O, in (x,O,y) . We want to compute the electric field created by the 3 charges on the axis z, passing by O and perpendicular at (x,O,y), thus computing the electric field...
  37. M

    MHB Inscribed circle in the triangle

    In the triangle a point I is a centre of inscribed circle. A line AI meets a segment BC in a point D. A bisector of AD meets lines BI and CI respectively in a points P and Q. Prove that heights of triangle PQD meet in the point I. I've tried to show that sides of triangle PQD are parallel to...
  38. O

    MHB Triangle Inequality and Convergence of ${y}_{n}$

    Let ${y}_{n}$ be a arbitrary sequence in X metric space and ${y}_{m+1}$ convergent to ${x}^{*}$ in X...İn this case by using triangle inequality can we say that ${y}_{n}\to {x}^{*}$
  39. Acemave

    Finding the Center of Mass of a Triangle

    Homework Statement a thin uniform wire is bent to form two equal sides AB and AC of triangle ABC , where AB=AC=5cm . the third side BC , of length 6cm is made from uniform wire of twice the density of the first . the distance of centre of mass from A is ? Homework Equations x centre of mass...
  40. B

    Trigonometry triangle Question

    For the triangle shown in the below image, ##\sin 60° = \frac{opposite}{hypotenuse} = \frac{y}{r}## ##\sin 30° = \frac{opposite}{hypotenuse} = \frac{x}{r}## The questions are: 1. What is the opposite and hypotenuse of sin 90°? 2. I am guessing that the opposite and hypotenuse of sin 90 is r...
  41. B

    Determining Precisely Which Angles of a Triangle Are Congruent

    Hello, Suppose that I have two triangles ##\bigtriangleup ABC## and ##\bigtriangleup XYZ## that are known to be congruent by the side-side-side axiom, from which it follows that the parts are also congruent, such as the angles. My question is, how do I determine which of the three angles of...
  42. T

    Area of triangle on sphere problem.

    Homework Statement What is the area of a triangle on Earth that goes from the North Pole down to the equator, through the prime meridian, across the equator to 30 degrees east longitude, then back up to the equator? The radius of the Earth is about 6378 km. Homework Equations alpha + beta +...
  43. A

    MHB In the triangle ABC the point D lies on the side BC and point E on the side AB

    In the triangle ABC the point D lies on the side BC and point E on the side AB. BD = AC, AD = AE and AB ^ 2 = AC * BC. Show that \angle BAD = \angle CEA
  44. R

    What is [s]motion[/s] moment of inertia of an equilateral triangle?

    I am unable to find it.
  45. lucasLima

    Help proving triangle inequality for metric spaces

    So, i need to proof the triangle inequality ( d(x,y)<=d(x,z)+d(z,y) ) for the distance below But I'm stuck at In those fractions i need Xk-Zk and Zk-Yk in the denominators, not Xk-Yk and Xk-Yk. Thanks in advance
  46. A

    I Could there be only one lower and one upper triangle?

    I'm doing LU factorization in linear algebra. And in general, do i know that i got the right one, given that there are many ways to get the desired entries into zeros, but results in different upper and special lower triangles?
  47. M

    MHB Prove Triangle BAD = CEA: Tips & Maths Class Help

    In the triangle ABC a point D lies on the edge BC, E - on the edge AB. Aditionally, BD=AC, AD=AE and AB^2=AC\cdot BC. Prove that \sphericalangle BAD = \sphericalangle CEA. I have to do this task on Maths class on Monday and I need any tips or something because I don't know how to start it.
  48. Handsome jack

    How Can You Find Forces P, F, and T in a Static Equilibrium Problem?

    1. Homework Statement Find forces P,F,and THomework Equations Fx = 0 Fy = 0 The Attempt at a Solution So far I only got force T from getting the moment from point b. Don't know how-to start getting force P and F since they're both at the same point. Any help will be much obliged thank you [/B]
  49. modularmonads

    [Euclidean Geometry] Kiselev's Plainimetry Question 242

    Homework Statement Two lines passing through a point Μ are tangent to a circle at the points A and B. Through a point С taken on the smaller of the arcs AB, a third tangent is drawn up to its intersection points D and Ε with MA and MB respectively. Prove that (1) the perimeter of ▲DME, and (2)...
  50. anemone

    MHB Right Triangle: Proving It's a Right Triangle

    The sides $x,\,y,\,z$ of a triangle satisfy the equality $(x^4+y^4+z^4)^2=2(x^3+y^3+z^3)$. Prove that it's a right triangle.
Back
Top