Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [triangles]

For questions about properties and applications of triangles.

A triangle is a polygon with three sides. It is an important geometric figure, because any polygon can be subdivided into triangles.

Triangles can be classified by the number of sides they have that have equal length

  • All three sides of an equilateral triangle have equal length.
  • An isosceles triangle has at least two sides of equal length.
  • A scalene triangle is a triangle that is not isosceles, that is, it has no sides with equal length.

A triangle may also be classified by describing its angles. A triangle is said to be a right triangle if it contains a right angle, and obtuse triangle if it contains an obtuse angle, or an acute triangle if all three of its angles are acute.

6703 questions
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Is ABC an equilateral triangle

In the figure, AD=BE=CF. Moreover, DEF is an equilateral triangle. Must ABC be equilateral?
Steven
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Pythagorean Theorem for imaginary numbers

If we let one leg be real-valued and the other leg equal $bi$ then the Pythagorean Theorem changes to $a^2-b^2=c^2$ which results in some kooky numbers. For what reason does this not make sense? Does the Theorem only work on real numbers? Why not…
MyNameIsKhan
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Is there an equation that represents the nth row in Pascal's triangle?

I'm doing binomial expansion and I'm rather confused at how people can find a certain coefficient of certain rows. For example, if a problem was $(2x - 10y)^{54}$, and I were to figure out the $32^{\text{nd}}$ element in that expansion, how would I…
yuritsuki
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Prove that no three of the six angles trisectors meet at one point

I.e., that there are 12 distinct intersection points of the angle trisectors. $ABC$ is a triangle: with its 6 angle trisectors. Prove that $M, N, O, P, Q, R, S, T, U, V, W, X$ (the trisector's intersections) are all distinct. The only formula I…
TNT1288
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Maths exam question on consecutive Pythagoras triplets

Our 13 year old daughter brought home this maths question that she was asked in a "maths challenge" last week: Q. The values of the adjacent and opposite sides in a right angle triangle of lengths 3, 4, 5 are consecutive. Obtain another triangle…
user1682654
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Show that points in plane lie within the interior or on the boundary of a triangle with area less than $4$

"Consider finitely many points in the plane such that, if we choose any three points A,B,C among them, the area of triangle ABC is always less than 1. Show that all of these points lie within the interior or on the boundary of a triangle with area…
Pookie
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Geometry Proving Isosceles Triangle

This question seems tricky and I frankly don't know how to start. I will be grateful if someone can provide a solution. We have a triangle $ABC$ and there is a point $F$ on $BC$ such that $AF$ intersects the median $BD$ at $E$. If $AE=BC$ how do we…
Nitesh
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Lengths of the sides of a triangle: sufficient and necessary condition?

For any three positive scales, $a,b,c$, what is the sufficient and necessary condition such that they can form a triangle? Is $a+c>b,a+b>c,b+c>a$ enough? Thanks!
Jingjings
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How is the hypotenuse the longest side of any right triangle?

I see that the hypotenuse of a right triangle is opposite the right angle, but how is it always the longest side? I also know that it connects to endpoints of other sides. Please help me out with this! I'm really wanting to know this surprising…
Mathster
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Is there an integer that $\sqrt{3}$ can be multiplied by that will produce a whole integer?

The question came up while messing around with graph paper. I wanted to make an isosceles triangle where the length of one side and it's hight were both integers. The closest I could get was a base side of $8$ and a height of $7$. Which gives a…
mark howe
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If $P$ is any point on a straight line drawn through the vertex $A$ of an isosceles triangle $ABC$, parallel to the base, prove that $PB+PC>AB+AC$

$C$ and $D$ are two points on the same side of a line $AB$ and $P$ is any point on $AB$. $PC+PD$ is least when the angles $\angle CPA$ and $\angle DPB$ are equal. I am not able to figure out as to how we can prove this. It would be great if…
Ishita Hariramani
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Incentre of the triangle proving

A straight line is drawn through the incentre I of the triangle ABC perpendicular to AI meeting AB, AC in D and E respectively. Prove that BD.CE=ID^2
Apoorv Jain
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Triangle ratio of areas

This is a photo that was originally posted on Google Plus. I would like to know how to solve for S. I started by splitting S into two parts S1 and S2 by drawing a line from A to M. I also know that I should use the fact that since the triangles…
Quaxton Hale
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What's the minimum number of information required to solve a triangle?

In school, I was always taught that given 3 pieces information with at least the length of one side, it was possible to determine all the measures of a triangle. However, I recently stumbled on the following problem, to which I found two…
Samuel Martineau
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Finding the distance between two gears

I have the following problem: In my class, we did a majorly complicated method to figure this out but I think there is a better way to do this... Here is the exact problem: A belt fits snugly around the two circular pulleys shown. Find the…
Freesnöw
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