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.

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$ABC$ is a triangle and $X$ is any point such that $\text{ar}(\Delta AXB) =\text{ar}(\Delta XAC)$ , find the locus of $X$.

I know that if sides $AB$, $AC$ and $BC$ are extended at a constant rate the position of $X$ remains the same. However I don't know what the locus of this would be . (I haven't studied the topic locus I'm in class 9 any help would be highly…
Deveshi Singh
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Midpoint of a segment

Let ABC be a triangle, I and J are two points such that : $\overrightarrow{AI}=\frac {2}{3}\overrightarrow {AB}$ and $\overrightarrow{AC}=\frac {1}{2}\overrightarrow {AJ}$. (BC) and (IJ) intersect in O. Show that O is the midpoint of the segment…
سعيد بلقاضي
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Point in the interior of a triangle

Let $P$ be a point in the interior of triangle $ABC$. The lengths of $AP, BP,$ and $CP$ are $3, 4,$ and $5,$ respectively. Find the value of $AB^{2}$ if $AC = 7$ and $CB = 8.$ I tried using heron's formula but I ended up with a $4$th degree…
SuperMage1
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A triangle inequality and probability problem.

Here is the problem: Real numbers $x$ and $y$ are chosen independently and uniformly at random from the interval $[0, 1]$. What is the probability that $x, y,$ and $1$ are the side lengths of an obtuse triangle? Round your answer to the nearest…
Max0815
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How the triangle definition relates with its existence

In Plane and solid geometry by Fletcher Durell(p.32), it states that: A triangle is a portion of plane bounded by three straight lines, as the triangle ABC". How does this statement relates with the existence of a triangle. For example, how…
justin
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Complete tesselation of sphere with hexagons

I'm working on making the hexagons tessellated sphere using the fully procedural/programmed approach. Basically I'm following the guidance @coproc gave as a reply to the question here:…
lhog
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Finding the point on line where two points join at equal angles to a perpendicular line

Im not sure what this would be called and how to explain it properly, so I drew an image to represent what I mean: (cant embed it yet) https://i.stack.imgur.com/0QKge.png Basically, I want to find point C where the angles from a perpendicular line…
KingDragonRider
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Does the angle bisector always pass through the midpoint of any line segment between the two sides of the angle?

Consider this image: will the angle bisector of angle AOB always pass through the midpoint of AB, regardless of the lengths of AO and BO?
AndyPerlitch
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In a triangle $a:b:c =4:5:6$, then $3A+B$ equals to?

In the above question $a,b,c$ are sides of triangle and $A,B,C$ are angles. The correct answer is $\pi$ but I am getting $\pi - C$.
Muhammad Ali Zafar
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Relation between circum radius, inradius and the angles.

Is there any relation between circumradius, inradius and the angles associated with a triangle? Any help will be appreciated.
Chandramauli Chakraborty
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Pentagons and Triangles

If you have a regular pentagon with all equal sides and you split that pentagon into 5 triangles (inside of that pentagon) would the triangles be equalateral or not?
Missmaxx
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How do I prove the sides equal in this question?

If the angular bisector of an angle of a triangle bisects the opposite side, prove that the other two sides are equal. This was the question written in my math book. I know there is a theorem related to this, but I can't understand that. I am a 9th…
Robin
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Sine rule question…

Sine rule: $$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{C}{\sin(C)}=2R$$ But I want to know what is $$\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}=?$$ On wikipedia it says it is equal to $\dfrac{2\Delta}{abc}$ shouldn't it be simply $\frac…
user402003
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Can a triangle have a side length of zero?

I am writing a program that determines the type of triangle it is based on the three side lengths. I think I have covered all the bases with one exception that I am not sure of. A triangle with all sides of zero is it a triangle or not? Following…
Yodilicious
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Can I get the triangles area by squares of sides?

In triangle $\triangle ABC$, let $D$, $E$ and $F$ be the midpoints of $BC$, $CA$, and $AB$ respectively and let $G$ be the intersection of $AD$ and $BE$. If $AG = 15$, $BG = 13$, and $F G = 7$, what is the area of triangle $\triangle ABC$? So…
M. Chen
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