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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Barycentric Coordinates in a Subtriangle

Given a triangle formed by vertices $v_{0},v_{1},v_{2}$, a point inside of it, $P$, with barycentric coordinates $u,v,w$ and the sub-triangle $S$ formed by the midpoint of triangle edge ($m_{01},m_{12},m_{02}$): What are the barycentric coordinates…
Xaldew
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Consider the points $P(0, -2, 0), Q(6, 1,-2), R(2, 4, 1)$, Find the area of the triangle PQR.

Consider the points below. $$P(0, -2, 0), Q(6, 1,-2), R(2, 4, 1)$$ Find the area of the triangle PQR.
ÆMJÃD Sarfarazi
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Figure inscribed inside a circle.

In the given figure, find the $MO\times MS$ of the circle: Given that $MP = 16$ and $MQ = 10$ I know I have to prove $\triangle PSM$ and $\triangle NQM$ similar to get ratio.
Arya
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Formula for angles $ \left({\cot}^{-1} \left(\frac{{AD}-{AC}}{{BD}}\right)-{\cot}^{-1} \left(\frac{{AD}}{{BD}}\right)\right)\cdot \frac{180}{\pi}$

If we have triangle $\varDelta ABC$, with base $AC$ and height $BD$,we can calculate the angle $\angle ABC$ expressed in degrees,with the formula $$ \left({\cot}^{-1} \left(\frac{{AD}-{AC}}{{BD}}\right)-{\cot}^{-1}…
Srbija
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What Angle Do I Need to Know?

I am utterly confused on what I'm supposed to do cause my teacher says to use what we know about supplementary and complementary angles to find the answer but $126° + 58°$ would equal $184°$ which would be neither $180°$ or $90°$. So how would I…
Nora Smith
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Altitudes Ratio

If h, h', h'' denote the lengths of the three altitudes of a triangle, which of the following ratios never occurs as the ratio h: h': h''? a)2 : 3 : 4 b)2 : 3 : 5 c)2 : 4 : 5 d)3 : 4 : 5 e)3 : 4 : 6 Any help would be much appreciated! If possible,…
Hummus
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Do all right triangles have the same angles?

I'm trying to find the complementary angles in a right rectangle and I've thought in these two triangles: Do A and B have the same angles? At first, I thought so. But now, I'm not sure. I think the angles value depend on the length of segments c,…
VansFannel
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Iteration of the construction of Cevian triangles

Pick some triangle center. Construct the Cevian triangle. Consider its angles. If you want to iterate the construction (find the same triangle center for the Cevian triangle, and so on), the angles $\phi,\dots$ of the Cevian triangle should be a…
Hauke Reddmann
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In $\triangle ABC$ with $\angle A\;>\;\angle B\;>\;\angle C\;>\;\frac12 \angle A$, find the range for $\angle C$

In $\triangle ABC$, $$\angle A\;>\;\angle B\;>\;\angle C\;>\;\frac12 \angle A$$ Find the range for $\angle C$. By $$180^\circ=\angle A+\angle B+\angle C\;>\;\angle C+\angle C+\angle C\;=\;3\angle C$$ We can find the upper bound: $$\angle…
Cyh1368
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Prove that $PM^2 = QM . MR$

$PQR$ is a triangle right angled at $P$ and $M$ is a point on $QR$ such that $PM$ is perpendicular to $QR$. Show that $PM^2 = QM . MR$ I saw following proof somewhere. "Proof: since $PM$ is perpendicular to $QR$. Therefore $\Delta PQR$ similar to…
Mathematical science
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"Special" point in a $3$-$4$-$5$ right triangle

This is a question for my math seminar class. Let $T$ be a right triangle with sides having lengths $3$, $4$, and $5$. A point $P$ is called "special" is $P$ is the center of a parallelogram whose vertices all lie on the boundary of $T$. What is the…
user978757
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In any triangle, $b^2\sin(2\gamma)+c^2\sin(2\beta)=2ac\sin(\beta)$

Prove that any triangle, $b^2\sin(2\gamma)+c^2\sin(2\beta)=2ac\sin(\beta)$. Hello. I am very stuck on this problem. How could I go? Expand the double-angle sine but don't get to anything simpler. Also use that $\alpha+\beta+\gamma = 180$ to use…
eraldcoil
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Shrinking a triangle keeping all angles the same (for practical application)

I know that I should be able to find my answer with a search engine but I think I am not phrasing it correctly to get useful results. I also imagine that this has been answered before but again, can't find it. The problem I am making a slope (for…
Matthew Brown aka Lord Matt
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How do you identify the base & perpendicular of a right angled triangle.

It is easier to tell with this diagram But what about this one ? For triangle BDC. Here , how do you tell either BD or DC is base ?
S.M.T
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Can we consider 3 triangles in case of congruency

Q: The perpendicular bisector of the sides of a triangle AB meet at I. Prove that: IA = IB = IC By considering two triangles: We need to prove that $$ I A=I B=I C $$ Proof: In $\Delta$ BID and $\Delta$ CID $\mathrm{BD}=\mathrm{DC}$ (given) $\angle…
S.M.T
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