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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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what is wrong with following right triangle's hypotenuse's square reasoning

In the image given in the link, the square of the hypotenuse is 2ab. But it can't be true. I can't be true. I can't seem to find the reason. any help would be appreciated.
Nasir Aziz
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Simple geometry question involving the circumradius of a triangle.

Prove that $\sin(2A)\overrightarrow{OA}+\sin(2B)\overrightarrow{OB}+\sin(2C)\overrightarrow{OC} =0 $ Where $O$ is the circumradius of the $ABC$ triangle How to approach this type of problem? How do we demonstrate that for P ( a point in the…
SADBOYS
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How to make correct system of equations to solve for the angles in this triangle?

I'm trying to solve this triangle for $X$. Thereby, I've tried to make correct system of equations. What would be the correct equations? Here are the equations I can find In $\triangle ABC$, recalling that $\angle ACD = y$ $$48 + 24 + x + 12 +…
Hamilton
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What's the minimum area of this triangle?

I am not sure how to answer this, it is for a quiz that I am doing and my teacher hasn't specified how to answer this type of problem. I've tried distributing the $x$ out and I got $(x^2-4x+10)/2$ as my minimum area but it's saying I am wrong. I…
Manaswini Datta
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Problem with 2 similar right-angled triangles

There are two similar right-angled triangles, where known information is only one side from one, another side from the other triangle, they are not hypotenuse and right angles. Is it possible to find all the angles and sides of these triangles?
Gujche
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cut the following shape into 3, 4, 5, and 6 parts using only two cuts (use only straight lines)

[ From what I understand not all the shapes need to be triangles. We could manage up to 5 parts, but could not do the 6 parts.
dokidok100
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Triangle $ABC$ $XY$ parallel to $BC$

In a triangle $ABC$ $XY$ is drawn parallel to $BC$ cutting $AB$ and $AC$ in $X$ and $Y$, respectively.Prove that $BY$ and $CX$ intersect on the median through $A$. I have tried using Menelaus theorem on $\triangle ABO$ where $O$ is the intersection…
user591062
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Find 3th triangle coordinate when two coords the length of two sides and an angle is given

Hello mathematicians A friend and I tried to figure this out for a while. We tried a lot, but could not find anything. We have two given points (A and B) Two given lengths ($\overline{AB}$ = $\overline{BC}$) One given corner ($\alpha$) We want to…
Wofke
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Finding the radius of incircle.

Let $AD$ be an altitude in a right $\triangle ABC$ with $\angle A =90°$ and $D$ on $BC$. Suppose that the radii of the incircles of the $\triangle ABD $and $\triangle ACD$ are 33 and 56 respectively. Let $r$ bet the radius of the$ \triangle ABC $…
Badguy
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Is the line joining the circumcentre and the foot of the median perpendicular to that side?

This is the picture. Here, is the line SP perpendicular on the side BC?
tryingtobeastoic
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The pattern of possible numbers of non-congruent triangles for different size dot grids.

If I have four dots, arranged in two rows of two to make a square, and I draw a triangle by joining three of the dots, there are four triangles I can draw, but they are all the same shape (they are congruent). If I start with nine dots, arranged in…
PERCIVAL
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How angles opposite to the sides of an equiangular triangle influence the similarity of these sides?

I hope that the sides opposite to the angles of an equiangular triangle are called homologous sides because these sides are similar. I would like to know why angles opposite to the sides of an equiangular triangle influence the similarity of these…
justin
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Why homologous sides are sides opposite to homologous angles?

In Plane and solid geometry by Fletcher Durell, he mentions in page 34 that 91. Homologous angles of two mutually equiangular triangles are corresponding angles in those triangles. Homologous sides of two mutually equiangular triangles are sides …
justin
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Maximum area for minimum perimeter of a triangle

Does the fact that a triangle has the maximum area for a given perimeter when it is an equilateral triangle (Isoperimetric Property of Equilateral Triangles) imply that the ratio of a triangle's area to its perimeter will have a maximum when all…
John Singac
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Ratio of the sides of triangles

I am currently reading about the ratios of the sides of triangles. By basic proportionality theorem, I was able to prove that if DE || BC in a given triangle ABC, then: AD/DB = AE/EC And by triangles similarity, I was able to prove that if DE || BC…
cozew
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