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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How to find this angle? triangle

Triangle Image How do I find $\angle\,\text{BCD}$? We know that $\text{AD} =\text{BC}$. I just don't know how to find $\angle\,\text{BCD}$. I tried using parallel line but I just can't.
Jimmy
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Prove for isosceles triangle using rotation at specific point and $\alpha = 45^°$

(note: my mathematical knowledge is around high school niveau. So please explain mathematical terms or use simple language - thank you :)) I have this task description: $f(x) = e^{-x}$ tangent of $f(x)$ at $x = 0 \to t(x) = -x + 1$ $n(x) = x +…
uuu
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Proving Triangle

I spend so much time for proving this triangle and i still don't know. Question : Given Triangle ABC, AD and BE are altitudes of the triangle. Prove that Triangle DEC similarity with triangle ABC
Annita
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Finding angle in an equilateral triangular pyramid

Given an equilateral triangular pyramid (refer the below diagram) $\Delta ABC$ & $P$ is any point inside the triangle such that ${PA}^{2}={PB}^{2}+{PC}^{2}$, then $\angle BPC$ is - I am unable to think of how to do this question
Amritanshu
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Prove $a^2\cos B\cos C+b^2\cos C\cos A+c^2\cos A\cos B\leq2S.$

Prove that in any triangle inequality holds: $$a^2\cos B\cos C+b^2\cos C\cos A+c^2\cos A\cos B\leq2S.$$ Is gender inequality that occurs right triangle, not an equilateral triangle. For this reason I suspect you have used other ways different from…
medicu
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Nature of the $\triangle$

In $\triangle$ ABC, the $\angle BAC$ is a root of the equation $3^{1\over2} \cos x + \sin x = {1\over2}.$ Then what kind of triangle is the $\triangle$ ABC.
Ruddie
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No. of equilateral triangles required to completely fill a bigger equilateral triangle

$\triangle ABC$ is equilateral with side length=2.1cm Smaller equilateral triangles with side length=1cm are placed over $\triangle ABC$ so that it is fully covered. Find the minimum number of such small triangles. I am not getting it. How is it…
Rudstar
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Formula to calculate a length to a point on hypotenuse according to given angle

I have a right triangle: Height: y (value over 0) Width: y (value over 0) Angle: α (degrees, value between 0-90) I need to find out the formula to count the length of x.
W0lfw00ds
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tetrahedron height

I've got the next figure: Now I would like to calculate the height, so from D to the plane ABC. First, I've tried with a coordinate system, but it's to difficult to take these distances into account. Then I remarked that all the faces (the…
Silke
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How many triangles can be created from a grid of certain dimensions?

How would you determine how many non-degenerate triangles can be drawn by connecting points in a $5 \times 5$ grid?
user2081893
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In Triangle ABC , BM and CN are perpendiculars from points B and C on any line passing through A. If L is the mid-point of BC, prove that ML = NL

I found this question in my textbook and I think this question requires the use of the mid-point theorem. I even tried proving the equality using congruence but couldn't seem to make a headway. I am in grade 9 so this might seem like a stupid…
MayankJain
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Given a triangle with two known vertices and the angle, get the coordinates of the last vertex

I have tried attaching an image of the triangle I am working with but since I am a new user this site will not let me post images (kind of defeats the purpose, but anyways). I have the following triangle: Point A = (x:40, y:100) Point B = (x:50,…
bushman_IL
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Proof of ASA , SAS , RHS , SSS congruency theorem

I have tried searching in many places for some good proofs of these theorems but couldn't find them anywhere . Even my math teacher cannot explain it to me and says that these theorems just work. I am a ninth grader so please try to explain in…
MayankJain
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Bound on difference between side lengths of a right triangle whose sides are pairwise coprime

Consider a right-angled triangle with integer-valued sides $a
tryst with freedom
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Pythagors Theorem : Geometrical interpretation

If x,y,z are the 3 sides of a right angled triangle, where say, x = hypo, y=vertical, z=base then I learnt that the area of a square on hypo = area of square on vertical + area of square on base i.e $$x^2 = y^2 + z^2$$ That's the usual picture…
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