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. karush

    MHB S4.13.t.71 angles of triangle PQR

    $\tiny{s4.13.t.71}$ $\textsf{For the given points $P(0,-1,2), Q(4,4,1), R(-4,4,6)$}$ $\textsf{Find the approximate measurements of the angles of $\triangle$ PQR. }$ $\textit{Ok, presume its get vectors first then use Dot Product...}$ $\textit{First find vectors $\vec{PQ},\vec{QR},$ and...
  2. A

    I Can a 63mm Bore Pneumatic Ram handle the required weight at an angled position?

    Hey So I am still a beginner in Physics and work asked me today to calculate if a 63mm Bore Pneumatic Ram will do the required job. Anyway, so I know how to calculate the weight capacity the ram can handle if it is at a 90 deg angle however if the ram is on an angle then I am stuck. I need to...
  3. A

    Finding net gravitational attractions in a triangle

    1. The problem is attached in a picture. I've done it five times and keep getting it wrong. The correct answer is also displayed in the picture. Thank you for any help. 2. Fg=Gm_1m_2/r^2 3. I calculated Fg between AB and BC (they are equal). So Fg=(6.67*10^-11)(4)(4)/(.10)^2=1.067*10^-10...
  4. M

    MHB Finding $\angle PCA$ in Triangle ABC with $\angle ANB = 90^\circ$

    In triangle ABC point $N \in BC$ , point $P \in AN$. Let $\angle ANB = 90$° $\angle PBA = 20$° $\angle PBC = 40$° $\angle PCB = 30$°. Find $\angle PCA$. I don't know how to solve that. Maby it was.
  5. A

    Calculating the area of equilateral triangle using calculus

    Homework Statement Calculating the area of equilateral triangle using calculus. Homework EquationsThe Attempt at a Solution The area of the triangle is the area of the circle minus 3 times the area of the sector shown in (light blue). So, the target is to calculate the pink area first...
  6. M

    MHB Possibilities for the side and angle of the triangle

    Hey! :o We have the triangle ABC with $c=18$, $\alpha=\frac{\pi}{6}$ and the median through $C$ has the length $5$. I want to determine all the possibilities for $a$ and $\gamma$. I have done the following: From the median we have the following...
  7. Z

    Area of Outer Triangle composed of two inner triangles

    Homework Statement 1. [/B]In the figure below, AB=BC=CD. If the area of triangle CDE is 42, what is the area of triangle ADG. See the attached figure Homework Equations I think we can start from area of triangle which is given by: Area of triangle CDE = ½ * CE * DE Or 42 = ½ * CE * DE...
  8. Pushoam

    Three points at the vertices of equilateral triangle

    Homework Statement Homework EquationsThe Attempt at a Solution The direction of motion of all the three particles are changing w.r.t. lab frame. But , their relative velocity remains constant. relative velocity = vb - va And the distance between the two particles decreases from a to 0. So...
  9. Z

    Find the lengths of the sides of the outer triangle

    Homework Statement [/B]What are the lengths of sides NO and OP in triangle NOP? See the attached figure Homework Equations [/B]I don’t think that the inner triangle is the 30-60-90 triangle so we can't use the eq of 30-60-90 triangle. However we can use the pythagorous formula to...
  10. jedishrfu

    B Great Magic Triangle Math Puzzle

    This is quite an interesting puzzle. You know it's wrong but you don't know why by inspection: http://twistedsifter.com/2017/07/profs-use-this-puzzle-to-teach-lesson-about-problem-solving/ Can you figure out an easy way to inspect it? I spotted one way.
  11. chopnhack

    Point charges in a equilateral triangle - typo in solution?

    Homework Statement Three point charges each carrying a charge of 11.0 µC are located at the corners of an equilateral triangle of side 15.0 cm. Calculate the magnitude and direction of the force on each charge. Homework Equations k = 9.0x109NM2C-2 F = k⋅(Q1⋅Q2)/r2 The Attempt at a Solution...
  12. Quantum Velocity

    I How Does the Hyperbolic Axiom Define a Maximal Triangle?

    I know that if a triangle have it edge // to each orther then it í the maximum triangle. Pls explain i don't understand hơ thí even possible
  13. haruspex

    B Counting intersections of lines in a triangle

    As a result of working on https://www.physicsforums.com/threads/area-of-hexagon-geometry-challenge.914759, this question occurred to me: Divide each side of a triangle into n equal lengths. Connect the ends of each length to the opposite vertex with straight lines, thereby forming 3n...
  14. G

    Explore Geometric Locus of Triangle Orthoprojections

    Homework Statement [/B] Given a general triangle ABC, find the geometric locus of points such that the three orthoprojection onto the sides of the triangle are aligned. Homework Equations Let's call A', B', and C' the orthoprojection of a given point M onto (AB) , (BC) , and (AC). M satisfies...
  15. H

    How to find the angles of a triangle in a semicircle?

    Homework Statement Homework Equations d(y)/d(x) --> max area area of triangle = 1/2 . base . height The Attempt at a Solution for number (2) [/B] x^2 + y^2 = r^2 --> circle equation base = 2R, height = y Area = 1/2 . 2R . y area = 1/2 . 4. √ (r^2 - x^2) area now is half of max = 2, so...
  16. H

    A circle is circumscribed around triangle ABC, find length?

    some formula related I tried to draw the problem can anyone give me clue how to solve it?
  17. M

    Finding an angle of a triangle as function of another angle

    1. Find α(β) given that the sum of the 2 sides= ##(x+y)## and its third, ##z## is a constant for 0<β<180. You can imagine that there's two pieces of string connected between two points. One string is as long as the distance between the two points while the other string is longer. If you...
  18. M

    MHB What is the perimeter of triangle ABC?

    The vertices of triangle ABC are A(1, 1), B(9, 3), and C(3, 5). 1. Find the perimeter of triangle ABC. I must use the distance formula for points on the xy-plane to find all three sides. I then add all three sides. Correct? 2. Find the perimeter of the triangle that is formed by joining the...
  19. FQVBSina

    I Triangle Numbers Algorithm: What is it?

    I was investigating the number of unique grid points in a Cartesian coordinate system if I were to start at a corner (say coordinate 1,1,1), and make one step in each of the three positive directions (coordinates 1,2,1; 2,1,1; and 1,1,2). Now I went from 1 point to 3 points. I repeat the same...
  20. HorseRidingTic

    Quadratics using Pascal's triangle

    Homework Statement The problem equation is contained in the picture. Homework Equations Pascal's Triangle is useful is this one. The Attempt at a Solution The difficulty I'm having is in going between lines 2 and 3 which I've marked with a little red dot. The closest I get to simplifying...
  21. Mateus Buarque

    Area of Hexagon - Geometry Challenge

    Determine the area of the painted hexagon, knowing that the area of triangle ABC is 120cm^2 IMG Link: https://m.imgur.com/a/WtdsW I tried using Heron´s formula, but just ended up with a bunch of terms and one more variable. Sidenote: I guess part of it is figuring out that the side lenghts...
  22. harpazo

    MHB Mass, Center of Mass, Triangle

    Find the mass and center of mass given the following region R. R: triangle with vertices (0,0), (b/2, h), (b,0) Let p = rho p = k The letters b and h as given in the points make it hard to find the equation of the lines needed for the inner upper and lower limits. I have worked this out...
  23. O

    Python Wave on string: How can I create a traveling triangle pulse?

    I have the following program that moves a wave on a string with fixed ends. The program solves the wave equation given a initial condition wave. The initial condition is a triangle wave splitting into two pulses. Here is the code written in Python: from numpy import * from matplotlib.pyplot...
  24. Z

    Reflection of triangle over a line

    Homework Statement How to rotate a triangle over a line? I have provided a attachment for it? Homework Equations Y= mx +c I don't know the eq for reflection The Attempt at a Solution My plan is find the eq of line. I have got points for the end points of the line but i don't know how to...
  25. Y

    MHB Finding Missing Angle Within A Triangle

    Can someone please help me with this question? Any help would be really much appreciated. Thanks all and have a great Easter!
  26. parshyaa

    Find the third coordinate of a vertex of an equilateral triangle

    Homework Statement Q. Prove that If (x1,y1) and (x2,y2) are the coordinates of the two vertices of an Equilateral Triangle then the coordinates of the 3rd vertex (X,Y) are $$X=\frac{x1+x2\pm\ √3(y1-y2)}{2},$$ $$Y=\frac{y1+y2\pm\ √3(x1-x2)}{2},$$ The Attempt at a Solution I used distance...
  27. M

    MHB What is the Perimeter of Triangle ABC?

    The vertices of Triangle ABC are A(1, 1), B(9, 3), and C(3, 5). Find the perimeter of Triangle ABC. I need to find the distance of AB, BC, and AC. I then must add all three distances to find the perimeter. Correct?
  28. T

    MHB Stuck on the sides of a triangle problem

    I have figured out the triangle's height and base, but I need to figure out sides a and b. I have tried Pythagorean theorem and similar triangle ratios, but it is not working out. Please help. See picture below. Thank you.
  29. lfdahl

    MHB Prove Triangle Inequality: $\sum_{cyc} \sin A$

    Prove, that for any triangle:\[ \sum_{cyc}\sin A - \prod_{cyc}\sin A \ge \sum_{cyc}\sin^3 A \]
  30. oohaithere

    Moment of Inertia of equilateral triangle about vertex

    Homework Statement A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. Homework Equations Slender rod, axis...
  31. I

    Maximum area of triangle inside a square

    Homework Statement ##ABCD## is a square piece of paper with sides of length 1 m. A quarter-circle is drawn from ##B## to ##D## with center ##A##. The piece of paper is folded along ##EF##, with ##E## on ##AB## and ##F## on ##AD##, so that ##A## falls on the quarter-circle. Determine the maximum...
  32. A

    B Basic geometry problem with triangle

    This is a problem I thought of, and I was wondering how to mathematically solve it with an equation. I tried calling one leg x. So the other leg, because of Pitagora's theorem, is: √(52 - x2) The area is equal to the product of the legs divided by two, so: 6 = (x * √(52 - x2))/2 12 = x * √(52...
  33. T

    Are My Proofs of Triangle Inequalities Correct?

    Just wondering if anyone could confirm if I've headed in the right direction with these (a) Prove the triangular inequality: |x + y| ≤ |x| + |y|. (b) Use triangular inequality to prove |x − y| ≥ ||x| − |y||. (c) Show that if |x − a| < c/2 and |y − b| < c/2 then |(x + y) − (a + b)| < c. So for...
  34. Dopplershift

    Limits of Integration of a Triangle

    Homework Statement Suppose you have a Triangle with the vertices, (0,0) (1,1) and (0,1). Integrating along that path. I have some differential function dZ where Z = Z(x,y) Homework EquationsThe Attempt at a Solution [/B] If I need to integrate, then I need to find the limits of...
  35. F

    I Proof that lattice points can't form an equilateral triangle

    From Courant's Differential and Integral Calculus p.13, In an ordinary system of rectangular co-ordinates, the points for which both co-ordinates are integers are called lattice points. Prove that a triangle whose vertices are lattice points cannot be equilateral. Proof: Let ##A=(0,0)...
  36. M

    MHB Calculate Area of Triangle ABC

    Point A(3, 4), point B(8, 5) and point C(7, 8) are located in quadrant 1 and form Triangle ABC. Note: Point A(a, b) Point B(c, d) Point C(e, f) Find the area of Triangle ABC using the formula below. A = (1/2)(a*d - c*b + c*e - e*d + e*b - a*e) I think this is just a plug and chug problem...
  37. M

    MHB Is the perimeter of a right triangle equal to its area? (Part 2)

    A right triangle is given. One leg is u units and the other leg is v units. The hypotenuse is given to be w units. If u = [2(m + n)]/n, v = 4m/(m - n), and w = [2(m^2 + n^2)/(m - n)n, show that (1/2)(uv) = u + v + w I must multiply u times v times (1/2), right? I then must add u + v + w. The...
  38. M

    MHB Can Pythagoras' Theorem Prove this Right Triangle Hypotenuse Equation?

    A right triangle is given. One leg is u units and the other leg is v units. The hypotenuse is given to be w units. If u = [2(m + n)]/n and v = 4m/(m - n), show that w = [2(m^2 + n^2)/(m - n)n. Must I square u and v to show that w = [2(m^2 + n^2)/(m - n)n?
  39. A

    MHB Area of Triangle with Given Data

    For b) area of AEF so one side is 7 - don't know how to get other 2 sides not sure if right triangle; don't think so how to use the data given since two of sides are slanted
  40. A

    MHB What is the multiplier for finding the area of triangle ADG?

    Not sure how to use a single area and line segments that are same to calculate the areas and line segments for the areas.
  41. A

    MHB Can you find the length of ON using Pythagoras and similarity?

    In attached file, I understand 50 is the base; no idea how to use the 24 height to calculate length of ON - must have to do with property of right triangles?
  42. R

    Circle inscribed in a triangle exercise

    Homework Statement In the drawing you can see a circumference inscribed in the triangle ABC (See the picture in the following link). Calculate the value of X https://goo.gl/photos/CAacV2dJbUrywfXv92. The attempt at a solution It seems I found a solution for this exercise with the help of a...
  43. J

    Finding the center of mass of an arbitrary uniform triangle

    Homework Statement 1. Show that for an arbitrary uniform triangle ABC, with A at (x1, y1), B at (x2,y2), C at (x3, y3), the CM (xcm, ycm), is simply defined by xcm=(x1+x2+x3)/3, and ycm =(y1+y2+y3)/3 Homework Equations xcm = 1/M * ∫xdm ycm = 1/M * ∫ydm M = ∫dm = ∫δdA where δ = M/A = dm/dA...
  44. S

    MHB How do I construct this Triangle?

    I have to construct the triangle "J" only using protractor, ruler, compass and pencil. But I can't seem to find a way to figure out the angles. Please help.
  45. M

    MHB Prove Equal Area Triangle & Parallelogram, $\angle ADC=90^{\circ}$

    Workings $\triangle ADE \cong \triangle CFE \left(AAS\right)$ $\angle AED = \angle CEF $( vertically opposite angles ) $\angle CFE= \angle EDA $( alternate angles ) $AE=EC $( E midpoint ) $ii.$ADCF is a parallelogram because diagonals bisect each other. Where is help needed How should...
  46. Const@ntine

    Comp Sci Fortran: Find a triangle's side, plus angles

    The statement: In every ABC triangle, the laws of sine (a/sinA = b/sinB = c/sinC) & cosine (c2 = a2 + b2 -2*a*b*cosC) are valid, where a, b & c are the sides opposite to A, B & C respectively. Write a program that calculates and prints on the computer's screen, the length of c, and also the...
  47. karush

    MHB *8s6.12.7 Find the lengths of the ides of the triangle PQR

    $\tiny{s6.12.7 Linkedin}$ a. Find the lengths of the ides of the triangle PQR. b. Is it a right triangle? Is it an isosceles triangle? $P(3,-2,-3), Q(7,0,1), R(1,2,1) PQ =\left|\sqrt{(3-7)^2 +(-2-0)^2+(-3-1)^2}\right|$ this is just an intro to vector calculus to get the basics of calc III
  48. Albert1

    MHB Finding the Area of Triangle ABQ in Rectangle ABCD with Given Points and Lengths

    Rectangle $ABCD$ ,point $P$ on $\overline{AB}$ and point $Q$ on $\overline{DP}$ respectively given: $\overline{AB}=14,\overline{CP}=13$. and $\overline{DP}=15$, if $\overline{CQ}\perp \overline{DP}$ on $Q$ please find the area of $\triangle ABQ$
  49. C

    MHB Area of a Triangle from 3 sides

    Can I have an opinion on this question, please? Personally I would use the cosine & sine rules to work out the angles then use trig to calculate the height. However, the question asks for Pythag to be used. Can someone please explain what method I should be using to answer this? Thanks Thanks Carla
  50. Z

    What is the exterior angle of a triangle?

    Homework Statement It looks as if 50 degrees is an external angle of the triangle.So it should be greater than the two opposite interior angles (i.e x and the other one). But book tells a different answer. Somebody please guide me.Zulfi. Homework Equations No eq. Rule: Exterior angle of a...
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