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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Geometry and property of triangle

$ABC$ is a cyclic triangle and bisector of angle $B\widehat{A}C$, $A\widehat{B}C$ and $A\widehat{C}B$ touches circle at $P$, $Q$ and $R$ respectively then measure of angle $R\widehat{Q}P$ is? The options…
AMIT KUMAR ANSHU
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geometry - prove that you can make new triangle with..

I have a triangle, the length of heights are $i,h,g$. Prove that we can build a new triangle so that the lengths of the sides are: $i^{-1}, g^{-1}, h^{-1}$ (see picture)
Omar Abu Asbe
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Mid-sections and angles

In the triangle $ ABC $, whose $ AC> BC> AB $, on the sides $ BC $ and $ AC $ chose the point $ D $ and $ K $, respectively, so that $ CD = AB $, $ AK = BC$. Points $ F $ and $ L - $ midpoints $ BD $ and $ CK $ respectively. Points $ R,S - $…
Roman83
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How/why does this proportion work?

In this diagram, ΔXYZ is inscribed into the circles. O is the center of the larger circle. OZ=x, altitude XO=x-5, and OY=x-9. ∠XOZ and ∠XOY are both right angles. Using the two similar right triangles OYX, and OXZ, this proportion can be written:…
Dana
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Finding the altitude of an isosceles triangle with base length and angle

So I have triangle ABC where: $AC = BC$; $AB$ is known $\hat C$ (the angle $A\hat CB$) is known I'm trying to find the altitude of said triangle.
AlienNova
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Finding 3rd Point of Isosceles Triangle

Im trying to find a way to calculate the position of the one of the base points of an isocicles triangle if I know the positions of the other two points, the angle measures, and the side lengths. It must be possible since you know everything else…
j76goatboy
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How to find a valume of a prism when when we are not given the height?

So I was learning how to find the surface area and volume. I came across few youtube tutorials which were simple. And in my book I found much harder problem. It asks me to find the volume of the prism when I'm given all sides of base instead of…
Limpuls
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Points of squares from triangle sides on circle

Taking a course on geometry, got this problem in my problem set. Suppose we have a triangle ABC and we take squares $BCP_1P_2$ and $ACP_3P_4$ such that $P_1, P_2, P_3, P_4$ are all on the same circle. How many positive integer triples of angles
user290610
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Solving the Height of a Triangle at a Point

I just solved a right triangle with all the angles and measurements: I want to find the height of the triangle at 2ft: How would I find this and what would the height be?
JohnDoe
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Equilateral triangle on the argand diagram

Let $P=3+2i$ be a point in the plane. Find points $Q$ and $R$ such that $PQR$ form an equilateral triangle with the center (of the triangle) at the origin. Does anyone know what to do?
Henry Newton
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Right angle triangle only area given

A right angle triangle has area 6 cm square. Is it possible to find the perimeter of the triangle?
ClemKY
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Proving question on triangles.

I have a question that seems very difficult to solve by myself: Question: ABC is a triangle where B=2C. D is a point on BC such that AD bisects BAC and AB=CD. Prove that BAC=72°. Please help.
codetalker
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a question on "basic triangle at q"

Could someonehelp me to understand these sentences: A “basic triangle at $q$” will mean a triangle which has the sides adjacent to the vertex $q$ of equal length and an angle at $q$ of measure $30$. The height (or bisector) at $q$ will be used to…
Paul
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Is there enough information to answer this question?

My daughter got this question and I cannot solve it - or even give her direction. It appears there in not enough information. the number of equilateral triangles of side 1 into which an equilateral triangle of side n can be divided? ( n is a whole…
kovenlo
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How to scale a triangle such that the distance between original edges and new edges are equal?

This is very similar to this question: Coordinates of parallel triangle with a distance of 'd' between the parallel edges? That seems to provide the answer in 2D, but I am unsure how to apply this to 3D. To recap the original question; I am looking…
dmarra
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