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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Equilateral triangle trisected

In an equilateral triangle $ABC$ the side $BC$ is trisected by points $D$ and $E$. Prove $9|AD|^2 = 7|AB|^2$.
Kartik Ohri
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Finding an unknown length in a triangle.

I have incurred a question and I am having a hard time with it. Please refer the image below Here it is given that $AP:PC = 3:4$, $QM:MP = 3:2$ and $QB=12cm$. We have to find the length of $AB$. I have tried as many theorems I knew but was not able…
Mayank Mittal
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Prove equilateral triangle in another triangle

We got triangle $ABC$ ($AC = BC$). ∠$ACB = 120^\circ$. $AM = MN = NB = \frac 13AB$. Prove that CNM is equilateral triangle. Any ideas how to do that? I'd be grateful if someone helps me! P.S.I am sorry that the drawing is not very accurate!
SuperMan
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Shortest length of line segment that bisects triangle in two equal area

A segment of a line $PQ$ with its extremities on $AB$ and $AC$ bisects a triangle $ABC$ with sides $a,b,c$ into two equal areas, then find the shortest length of the segment $PQ$. I was looking for small hint as how to approach this question? I am…
Ananya
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Find the lengths of sides of a right triangle

If I know the length of the hypotenuse of a right triangle ONLY, is it possible to find the lengths of the remaining 2 sides of that same triangle?
BloodDrunk
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Construct the triangle with given points and lines

On the following picture you see the excersice handed to us. Construct triangle ABC when you know that x is the line that contains points B and C, line z is the median that goes trough point A and point E is the start of the altitude going through…
Michelle_B
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Proving the Pythagorean Theorem with just variables

I basically have just three problems: a) How many similar triangles can you find in the figure below? b) Use part a) to prove the Pythagorean Theorem (note: to prove something you do need to use variables). c) Find the lengths of the 3 unknown line…
JustAKid
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value of X and Y from triangle

my son is in 6th grade and i am trying to help him solve this problem. but i want to understand so i can teach him. Write and solve equations to determine the value of x and y . triangle is given (PMN). $M$ is $13x$, $N$ is 65 deg, $p$ is not…
Mary jordon
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Angles sum in a triangle on the x- axis.

$\angle BCA=90$ degrees I probably do not understand the concept of angle sum in a triangle but here is the thing. $\angle BAC$ is negative by convention. So is $BCA$ going to be greater than 180 degrees? So this is obviously wrong(or is it?). I…
The Cryptic Cat
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Rational distances in triangle

Given triangle with sides of length $3, 4$ and $5$ prove that if $P$ is a point inside the triangle, then rationality of sum of distances from the point $P$ to the vertices implies rationality of sum of distances from the point $P$ to the sides of…
user263286
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Calculating Perpendicular and Base of Triangle. Suggestion

In this diagram AB and CD are both perpendicular to BE.If EC=5 and CD=4. What is ratio of AB to BE ? How would i go about solving this triangle (without trigonometric ratios). I could only get DE=3 using Pythagoras theorem and was stuck after…
MistyD
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Determine third point of Right Triangle when two points and all sides are known and $A\hat BC=90$

I have two points and all sides of right triangle I need find A point \begin{gather*} |AB| = 1 \\ |BC| = 1 \\ |AC| = \sqrt{1^2 + 1^2} = \sqrt2 \\ A(?,?) \\ B(0,0) \\ C(1,0) \\ \\ |AB| = 1 \\ |BC| = \sqrt{1^2 + 1^2} = \sqrt2 \\ |AC| = \sqrt{1^2 +…
MHA
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Do the properties of a pedal triangle hold good when the triangle on which the pedal triangle is constructed, an obtuse an triangle?

For Example, Can we assume that the incentre of a pedal triangle is the orthocentre of the triangle on which the pedal triangle is constructed in all cases?
Rishabh Kumar
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Find the Coordinates of a Unkown Point of a Triangle

The situation is as follows: I am creating a game in this game I have a line($A$ to $B$) and a mouse position $C$. Now I want to calculate point $D$ on line $A$$B$. I know the coordinates of: $A$, $B$ and $C$ and the angle of point $B$. It should…
Faas
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Find point given a line and two angles

Let's say I have two points $p_1=(x_1, y_1)$ and $p_2=(x_2, y_2)$, which are given as two points of a triangle $T$. And let's say I know the angles of $T$ at $p_1$ and $p_2$. How do I find the third point $p_3=(x_3, y_3)$ of $T$?
Vakey
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