Mathematics Stack Exchange
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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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Is there a triangle array that takes the preceding number and adds one for the first and subtracts one for the second term?

I was wondering if there is a triangle array that would produce 0 1,-1 2,0,0,-2 3,1,1,-1,1,-1,-1,-3 4,2,2,0,2,0,0,-2,2,0,0,-2,0,-2,-2,-4 where i becomes i+1, i-1 I'm looking for a way to determine if @ row x and position y the value is 0.
Mandelbrotter
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Can I find other angles of triangle If I have only 1 angle?

The problems goes like: "In a triangle there is inside angle B(beta) by 10 bigger than angle A(alpha). And agle Y(gamma) is 3 times bigger than angle B(beta). Define all angles." It's not stated what kind of Triangle it is, nothing. So is it even…
Samčo Kaprális
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number of such triangles, if feet of perpendicular are given

The coordinates of feet of perpendicular from the vertices of a triangle on opposite sides are $D(20,25),E(8,16),$ and $F(8,9).$ The number of such triangles are what i try we know that point of intersection of feet of perpendicular from vertices…
jacky
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Find the distance covered by a corner of the plate in one revolution round the fixed plate.

An equilateral triangular plate of side ‘a’ is rolling without slipping on the periphery of another identical fixed equilateral triangular plate as shown. Find the distance covered by a corner of the plate in one revolution around the fixed…
infinite-blank-
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Find distance between two points on Cartesian plane

I have a triangle on the Cartesian plane where I know the following: $$A = (X_1, Y_1)$$ $$B = (X_2, Y_2)$$ $$C = (X_3, Y_3)$$ $$\angle ABC = 90$$ $$\overline{AB} = x$$ $$\overline{AC} = 2x$$ I know A and B but I don't know C's location. Can I use…
yovel cohen
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how the test of similarity of two triangles confirm that they are similar?

For two triangles to be similar , their corresponding angles should be congruent and corresponding sides should be in proportion . But for given two triangles we don't always need to check whether their all angles are congruent and all corresponding…
Sameer Nilkhan
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relation between inradius and exradii of a triangle (Where did my proof go wrong?)

I am given a triangle $\triangle ABC$ with side lengths $AB=c$, $AC=b$, $BC=a$. $r$ is the radius of the incircle, and $r_a,r_b,r_c$ are the radii of the excircles. The incircle divides the sides of the triangle to $a=y+z$, $b=x+z$, $c=x+y$. $p$ is…
aradarbel10
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Sides of similar triangles

In the attached question, I am able to find x but not y. I know that sides of similar triangles are proportionate but that's not helping here. And I guess the third side of the smaller tringle would be (y+3)/2 but how to calculate y? X would 68…
aarbee
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Relation between triangle area and summed squared sidelengths

I am wondering if there are any interesting relations or interpretations between the total area of the squares and the triangle area? I am not looking for variants of Heron's formula. I am looking for a relation in the style: "the ratio between the…
granular_bastard
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In a $\Delta ABC$, if $r_1=1$ and $r_2=2$ and $C=\frac{\pi}{2}$, find area of triangle.

$r_1$ and $r_2$ are ex-radii about side a and b respectively. $\Delta$ is area of triangle. s is the semi-perimeter Since $r_1=\frac{\Delta}{s-a}$ $$\Delta=s-a$$ and $$\Delta=2(s-b)$$ From this, it can be observed that $$b-a=\frac{\Delta}{2}$$…
Aditya
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$L_1$ and $L_2$ are two rays drawn from A at an angle 30. A point B is taken at $L_1$ at a unit distance from A .

A perpendicular $BB_1$ is drawn rom B to $L_2$ and perpendicular $B_1B_2$ is drawn from $B_1$ to AB. Perpendicular $B_2B_3$ is drawn from $B_2$ to $AB_1$ and so on. Prove that $AB, AB_1 , AB_2$ are in a geometric progression. Here is the diagram I…
Aditya
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Triangles and Congruency

1.) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent. Is that SOMETIMES TRUE, ALWAYS TRUE, OR NEVER TRUE? I know that it is not NEVER TRUE. 2.) Two equilateral triangles with a pair of…
Vaibhav
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In $\Delta ABC$, find the value of $\frac{a\cos A+b\cos B +c\cos C}{a+b+c}$ in terms of $r$ and $R$

$$\frac{R(\sin 2A+\sin 2B+\sin 2C)}{a+b+c}$$ $$=\frac{R(4\sin A \sin B\sin C)}{2R(\sin A+\sin B+\sin C}$$ $$=\frac{8R\sin \frac A2 \sin \frac B2 \sin \frac C2 \cos \frac A2 \cos \frac B2 \cos \frac C2}{8R\cos \frac A2 \cos \frac B2 \cos \frac…
Aditya
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In $\Delta ABC$, if $A=60$ then the value of $(1+\frac ac +\frac bc)(1+\frac cb -\frac ab)$

So I cheated a bit in this question. Since there are no other conditions given, I assumed the triangle to be equilateral, and so the answer ends up being 3. Now I don’t have the right answer with me, but the options were 3,2,1,4 Is my answer right,…
Aditya
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Find 3rd vertex $(x,y)$ of a right triangle given vertexes $(x_P,y_P)$ , $(x_R,y_R)$, and all three sides

I want to find the x and y of the vertex P2 in below right angle triangle: I have tried Thales's theorem and triangulation but they all return a very complicated formula to calculate x and y with multiple answers. Since all the parameters of the…
Aboriginal
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