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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Calculating the length of a line in a triangle

I feel very stupid, but I have to answer this question but I cannot seem to solve it! :( I have to find the length of DF. I already figured out that because angle C = angle A1 (left part of the angle) Thales applies so AD must be 12 as well. But I…
Sanne
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Triangle geometry - lines that separate in two parts of equal area

Consider the set of lines that separate a triangle in two parts of same area. The three median belong to the set, in particular. What can be said of the envelope of the set of lines? For example, is the envelope a bounded set? Thank you for your…
galath
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Special Triangle

A triangle with integer sides a, b and 13 is given so that a is also a prime. The angle opposite to c=13 is 120° (m(C)=120°). Find a and b. The answer is a=7 and b=8. Howewer, how can we solve it using modular arithmetical analysis without trying…
mathwriter
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Finding the radius of the circumcircle when orthocentre, circumcentre and a side is given

My approach is as folow Hence as per the power rule the Centriod cuts the line joining Orthocentre and Circumcentre in the ratio 2:1 hence $G=(\frac{14}{3},\frac{23}{3})$ but this lies on the line $2x+y=17$ hence I presume that it is a typo error…
Samar Imam Zaidi
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Area of shaded region (2 triangles)

Find the area of the shaded region. I don't really have any idea how to do this. Is it possible to find the area or there is a lack of information to answer this question?
Magenta
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A problem related to areas of triangles

Consider a triangle ABC. there is a point P inside this triangle and BP and CP when extended meet AC and AB respectively at E and F. Prove that $[BPC]^2>[BPF][CPE]$ Here [.] denotes area of the polygon
Aarush Saharan
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Why is the largest angle of a $5$-$11$-$13$ triangle greater than $90^\circ$?

Why is is $x>90^\circ$? I thought that since we do not have the $5,12,13$ sides of a right triangle, the only way that's possible is the height of the triangle is leaning right, so $x<90$, but the answer key says that $x>90$. The only way I can…
user685056
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Angles of a pedal triangle

Found it while further playing with this question. Let $P$ be a point inside an acute triangle $ABC$ (whether it works for obtuse ones - I doubt it). Let $A'B'C'$ be the pedal triangle of $P$. Now assume that (with given constants $\lambda,\mu$)…
Hauke Reddmann
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is there an equation to find how many triangles exist in this?

In the image above which i horribly draw i am showing first a circle. The following "shapes" have small circles which represent points. All those points are positioned on the perimeter of that circle. Each and every point is directly connected…
user1008209
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Given the triangle is right-angled, find the value of a.

I am doing my schoolwork, and I can't figure out how to do this problem. I can't find anything related to it by searching it up, and the lesson name is just called 'Problem Solving', so I have no title to search it up with. How do you do this? The…
Wannabe Programmer
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Shortest distance between a point and a curved triangle

I am trying to find a nice formulation on how to calculate the distance between a point $(p_1, p_2, p_3)$ and a triangle in 3D, where the triangle is non flat (Strictly speaking it is not a triangle anymore, but I don't know the correct term for…
M. Denninger
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Sides of triangle from an inequality

Consider three real numbers $a \ge b \ge c \gt 0$. If $(a^x-b^x-c^x)(x-2) \gt 0$ for any rational number $x \neq 2$, show that $a, b, c$ can be the length of the three sides of a triangle $ABC$; $ABC$ is a right-angled triangle. My try: Since, for…
Debprasad Kundu
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Basic Proportionality theorem concept clarification

Basic Proportionality theorem states - if a line is parallel to a side of a triangle which intersects the other sides into two distinct points,then the line divides those sides of the triangle in proportion. So in triangle ABC AD/DB = AE/EC if DE…
Programmer
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Generating triangles with consecutive-integer sides and rational area

I'm stuck on this problem for quite some time: Call a triangle a Special Rational triangle if it's area is rational, and the side lengths are consecutive positive integers, Can we find a closed form which generates all Special Rational…
BooleanCoder
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Triangle Properties application

In a triangle ABC, AD is the altitude from A. Given b>c, $\angle C = {23^o}$,$AD = \frac{{abc}}{{{b^2} - {c^2}}}$. Then $\angle B = \_\_\_{\_^o}$ My approach is as follow $\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} = 2R$ $AD =…
Samar Imam Zaidi
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