What is Triangles: Definition and 215 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. J

    Statics and use of similar triangles

    Homework Statement How come all thetas are equivalent? Please take a look at this drawing http://tinypic.com/view.php?pic=2aahe3d&s=4 The Attempt at a Solution By similar triangles?
  2. P

    Related Rates (similar triangles)

    Homework Statement A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 ft from the base of the pole? Homework Equations...
  3. J

    About the number of triangles of convex n-gon

    Homework Statement Suppose that no three of the diagonal of a convex n-gon meet at the same point inside of a n-gon. Find the number of different triangles the sides of which are made up of the sides of the n-gon, the diagonals and segments of the diagonals. How to find it~@~? Homework...
  4. H

    Sine laws with Oblique Triangles: The Tower of Pisa

    Here's the question: The leaning Tower of Pisa leans toward the south at an angle of 5.5°. On one day, its shadow was 90m long, and the angle of elevation from the tip of the shadow to the top of the tower is 32°. Determine the slant height of the tower. How high is the tip of the tower...
  5. M

    Resistance of infinite nested triangles

    Homework Statement Here is an interesting problem... there is a wire bent in the shape of an equilateral triangle, side length = a and resistivity = rho. In the center of this triangle is another equilateral triangle (inverted, side = a/2, resistivity = rho) and so on into infinity. What is...
  6. T

    How Can Similar Triangles Simplify Solving for x and y?

    Homework Statement I've attached a diagram of the problem. Homework Equations Trig functions (soh cah toa) and pythagorus theorem a^2 + b^2 = c^2 The Attempt at a Solution I've tried a bunch of things but I can't find a start. I know I can't assume that triangle ABC is a right...
  7. Д

    How many right triangles can you create with given coordinates?

    Hello! I have one question. I have given 5 coordinates: 0 0 2 0 1 1 1 -1 3 -1 The question is how many right angles can I create with these coordinates? I know one way out, but it is pretty complicated. C52=5!/(2!*3!)=5*4*3!/(2!*3!)=10 And try every single combination (finding the...
  8. S

    Similar Triangles Formed by Diagonals of Quadrilateral in Circle

    Is it true that the diagonals of a quadrilateral inscribed in a circle split the quadrilateral into two sets of similar triangles? Is yes, how do we prove this?
  9. D

    How many triangles can you form with 21 evenly distributed dots?

    So, being inundated with the "How many triangles?" questions on Facebook, I noticed this one which is actually more difficult than I expect the question author intended: http://creative.ak.facebook.com/ads3/flyers/36/28/6002237517496_1_992e4bd8.jpg Assuming you have 21 dots evenly distributed...
  10. R

    Finding a triangles angles from its area + 2 sides

    Homework Statement A triangle had area of 21 cm² and two of its sides are 9 cm and 14cm long. Find the possible measures of the angle formed by these sides? Homework Equations Area= 1/2abSin(C) The Attempt at a Solution 1/2 (9)(14)Sin C = 21 --> Sin C = (1/3) approx 19.5...
  11. T

    Static Electricity and Triangles

    Homework Statement Three positive particles of charges 9.0\muC are located at the corners of an equilateral triangle with .15m sides. Calculate the magnitude and direction of the force on each particle. Homework Equations F=Kq1q2/d2 The Attempt at a Solution In class we haven't...
  12. M

    Differential of triangles and anlges

    Given cosine rule: L=\sqrt{(r_{1})^{2}+(r_{2})^{2}-2r_{1}r_{2}cosx} Consider a triangle with side lengths measured at r_{1}=3, r_{2}=4, and included angle x=\pi/2, each measured accurate to within 1%. Write down the differential dL in terms of dr_{1}, dr_{2} and dx, and use this to estimate...
  13. D

    Isoceles Triangle: Find Measure of Angle DFG

    Homework Statement triangle dfg and triangle fgh are isoceles. measure of angle fdh=28. dg=fg=fh. Find measure of angle dfg. Homework Equations The Attempt at a Solution
  14. M

    Congruent Triangles: Exploring the Possibilities

    Given a triangle ABC which is isosceles but not equilateral. That is, AB = AC, but AB does not equal BC. How many congruences are there, between triangle ABC and itself? Here's my answer: By the hypothesis, we can infer that triangle ABC is congruent to triangle ACB. So there is just one...
  15. R

    Vector proofs for triangles and some vector plane questions

    Homework Statement 1) Show by the use of vectors that the three altitudes of a triangle pass through the same point. 2) Show using vectos that the bisectors of the angles of a triangle pass through thr same point. 3)Find the distance from the point (1,0,-2) to the plane 3x-2y+z+1=0...
  16. B

    Calculating Volume of a Cylinder with Isosceles Triangles

    Homework Statement The base of S is a circular disk with radius r, Parallel cross-sections perpendicular to the base are isosceles triangles with height h, and unequal side in the base. Homework Equations A = 1/2 bh V = integral A(x) from [-r, r] The Attempt at a Solution x^2...
  17. L

    Derivatives of trig functions and isosceles triangles.

    The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is 100 cm2? I wasnt really sure where to start on this question so i tried my best at an answer. I'm sure I've gone wrong with this...
  18. U

    How do I solve triangles in 3D with specific vertices?

    How do i find the angles in the triangle with the vertices at [2,-1,0], [5,-4,3], and [1,-3,2]. This problem has been bothering me because when i find the angle between the vectors it only adds to roughly 110 degrees, and that cannot be right.
  19. M

    Find the point D such that all the triangles have the same area.

    Consider \triangle ABC with vertices A(4,8),B( - 1,2), and C(0, - 3). Find the point D such that \triangle ABD,\triangle ACD and \triangle BCD all have the same area.
  20. L

    Right Triangles within a right triangle. (Trig)

    "To Estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32 degrees. One thousand feet closer to the mountain along the plain, it is found that the angle of eleveation is 35 degrees. Estimate the height of the mountain."...
  21. A

    How to Find the Area of Quadrilateral BEFC in an Equilateral Triangle?

    Homework Statement ABC is an equilateral triangle with sides of 2 cm. BC is extended its own length to point D and point E is the midpoint of AB. ED meets AC at F. Find the area of quadrilateral BEFC in square centimeters in simplest radical form. Show all work and clearly label figure(s)...
  22. Z

    Centroids of various triangles.

    I've been having some confusions regarding the centroid coordinates of triangles. I've been taught that the centroid of a triangle lies at 1/3rd of the perpendicular distance from any selected base to the corresponding top point of the triangle. I tried to use this shortcut to find the...
  23. rocomath

    Area, approximating triangles?

    Let A_n be the area of a polygon with n equal sides inscribed in a circle with radius r. By dividing the polygon into n congruent triangles with central angle \frac{2\pi}{n}, show that A_n=\frac 1 2 \pi r^2\sin{\frac{2\pi}{n}}. Ok, I drew a circle with congruent triangles inscribed in it. I...
  24. D

    Proving the Converse of the Intersecting Chords Theorem: Inside the Circle Case

    Hi, do anyone know a proof of this converse: "If, A,B,C,D,E and F are points in the plane and \frac{AB}{BC}=\frac{DE}{EF}, then triangles ABC and DEF are similar."
  25. L

    Derivatives (Trig) with Isosceles Triangles

    1. THe base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At whate rate is the base angle increasing when the area is 100 cm^2? answer 0.05 rad/s 2. What I did: -Took the derivative of tan and assumed that each base side of the trianlge was 10 cm...
  26. L

    Derivatives of Trig with Triangles

    [SOLVED] Derivatives of Trig with Triangles 1. Two sides of a triangle are six and eight metres in length. If the angle between them decreases at the rate of 0.035 rad/s, find the rate at which the area is decreasing when the angle between the sides of fixed length is pi/6. Answer 0.727 m^2/min...
  27. rocomath

    Finding X: Solving for Points on a Circle with Given A and B Values

    Two points, A and B, are given in the plane. Describe the set of points X such that: AX^2 + BX^2 = AB^2 I'm not really sure how to start this off. I've drawn the circle and a line going from A to B with a midpoint AB at the origin (AB). I also, solved for X which is...
  28. R

    Proving two sides of equation for triangles

    [SOLVED] Proving two sides of equation for triangles Homework Statement In angle ABC, which is an isosceles triangle with <B = <C, show that 2cot(a) = tan(b) = cot(b) Homework Equations tan2a = 2tana / 1 - tan^2 a tan (x - y) = tanx - tany / 1 + tanx tany The Attempt at a...
  29. E

    Isocleles Triangles in a Parabola Help

    Homework Statement Triangle OAB is an isosceles triangle with vertex O at the origin and vertices A and B on the parabola y = 9-x^2 Express the area of the triangle as a function of the x-coordinate of A.Homework Equations A = 1/2 bh Distance formula (maybe) Heron's Formula (an...
  30. P

    How can the centroid and triangle angles help prove equilateral triangles?

    I found this problem off of mathematics magazine and I want to give it a try solving it, but I'm lost for ideas. The problem states the following: Let G be the centroid of triangle ABC. Prove that if angle BAC = 60 degrees and angle BGC = 120 degrees then the triange is equilateral. My...
  31. A

    Solve Oblique Triangles using Logarithms - Check Answers

    Any Help ? Solve the following right triangle by logarithms : A= 28°30', b= 18.3 units and solve the following oblique triangles, too : 1)a= 31, b= 15, c = 17 2) a=23.47, B= 115°30', C = 20° 29' I have already done my calculations but I need a check ! Thanks
  32. S

    Usefulness of Euler line in triangles?

    Is the Euler line in triangles USEFUL for anything in real life? This is the line which contains the concurrency points for the intersections of the triangle perpendicular bisectors, the medians, the altitudes, but not the angle bisectors. Interesting stuff, but are these points which occur on...
  33. E

    How Many Equilateral Triangles are Needed for Perfect Coverage?

    Homework Statement We are using a drawing program in computer and we place x number of identical equilateral triangles(of same length of edges) randomly. So whenever we choose a triangle on the screen randomly(each has an equal number of possibility of being selected), we can slide the other...
  34. T

    GCSE Proof os square with equalaterial triangles

    Homework Statement ABCD is a square and on side BC an equalaterial triangle is made extending to vertex E and another is made on line DC extending to vertex F. Prove that ECD is congruent to BCF. Homework Equations Proof is all about using algerbra to prove somthing right? If it's...
  35. B

    Do 3-4-5 Triangles Have to be 30-45-90?

    Homework Statement Hey, I have quick question. I tried looking on google, but couldn't quite reassure myself. Does a 3-4-5 triangle have to be a 30-45-90 triangle? Can the angles be any angle?(this is what I think...but not confident). I have a triangle(this is actually a physics...
  36. L

    Solving Angle & Triangle Problems: 2Tsin(angle) = 3mg

    THis isn't exactly a question however, its a method my teacher talked to me about and I don't quite understand. This is a way of getting greater accuracy, and attaining the higher grades. The question states, tan(angle) = 3/4 So instead of using tan^-1 (3/4) to get the angle with many...
  37. L

    Logarithms and triangles help

    Homework Statement Define a, b, and c as the sides of a right triangle where c is the hypotenuse, and a > 1 and c > b+1 show that log_{c+b} a + log_{c-b} a = 2(log_{c+b} a)(log_{c-b} a) 2. Governing equations The Attempt at a Solution Should I assume that a=2 and c=b+2?!
  38. A

    Comp Sci Creating Triangles Using Do..While Loops

    Hey, Im pretty new to c++ so my knowledge is limited. I have been set an assignment to create the following triangles only using Do...While loops. I'm having difficulty trying to code it. The underscores are just their to illustrate spaces. 1 *_________________5 * 5__________* * * * 1 *...
  39. S

    Right angle triangles area of overlap calculation.

    For some time now I've set myself a goal I've yet to reach. For the first time I feel I've found a proper place to ask for help. I'm trying to devise a closed formula for the area of overlap of 2 arbitrary triangles from the known 6 vertexes' values. Naturally, inside the plane. In attempting...
  40. S

    Minimize vertices distance between triangles

    If I have two triangles in three dimensions with vertices a1,b1,c1 and a2,b2,c2, and want to overlay them such that the distance between corresponding verticies is minimized, i.e. such that the total distance between the sum of the distances between the vertices a1-a2, b1-b2 and c1-c2 are...
  41. B

    Geometry (circles and triangles) proofs

    I'm having some trouble with one particular geometry proof: From that I've drawn the following: http://img96.imageshack.us/img96/139/circle9we.gif \angle ADB = \angle CED (as \angle ADB and \angle CED are alternant sements) \angle CBD = 180 - \angle CED (1) (as they are opposite angles in...
  42. C

    Trig Question: Draw 2 Triangles, Find Sides & Area

    URGENT Trig question Okay I missed this lesson, so I don't really know what to do. I know it has to do with law of Sines/Law of Cosines. (but I think I can do all the parts involving that) 1)First Decide how many triangles can be drawn based on the information (my edit: I can do this)...
  43. A

    Angle-Angle-Angle conditions for proving triangles are congurent

    Why is there not an Angle-Angle-Angle (AAA) condition for proving triangles are congruent? Is it because, in congruent polygons, the corresponding angles and corresponding sides are equal? If there were an A-A-A method, the corresponding angles would be equal but the sides wouldn't...
  44. T

    Solving the "Impossible" Matchstick Triangles

    In "The Equation That Couldn't Be Solved: How mathematical genius discovered the language of symmetry" by Mario Livio, he poses the following problem on page 268: You are given six matches of equal length, and the objective is to use them to form exactly four triangles, in which all the sides...
  45. H

    Properties of triangles

    If I1,I2,I3 are the excentres of tringle ABC then prove that Area of triangle I1 I2 I3 >=4*Area of triangle ABC ?
  46. ceptimus

    Can Pythagorean Triangles Have the Same Area but Different Side Lengths?

    Pythagorean triangles are right angled triangles where each of the three sides is an integer length. The 3,4,5 triangle is the best known. Find three Pythagorean triangles that each have the same area.
  47. A

    Why are musical triangles triangular?

    Is there any physics reason why musical triangles are triangular, and not circles with gaps (or anything else)? Or is it just tradition.
  48. S

    Triangles, Bridges And Centripetal Space Habitats

    Making metal bridges from steel triangles is a very good idea because triangles are one of the strongest known shapes. My question is, would making a bicycle wheel-like space station's foundation braced with lots of triangles of whatever construction material is used(carbon fiber, aluminum...
  49. W

    Similar triangles, looking for demonstration

    I need an algebric proof of the theorem of similar triangles (C/c=A/a=B/b).
  50. A

    Find three different right-angled triangles

    How do you do this? Find three different right-angled triangles whose side lengths are all integers and whose area is 840 square units? Is there a method that could be used?
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