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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The equation of the hypotenuse of an isosceles right angled triangle

The equation of the hypotenuse of an isosceles right angled triangle is $$x + 3y = 3.$$ The right angle is at the vertex $C(−2, 0)$. (a) Find the two other vertices of the triangle. (b) Find the equation of the circumscribed circle of the…
Egshiglen Bat Erdene
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Similar triangles eventually

Through the A-peak of the ABCD square is built a right that crosses the country BC at the point P. The bisector(bisectrix) of the angle PAD crosses the side to the point L. Find DL + BP if AP = 5 cm
vili
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$(r_1 − r) (r_2 − r)(r_3 − r) = 4 Rr^ 2 $

We have to prove $(r_1− r) (r_2− r)(r_3− r) = 4 Rr^2$ I know the following formula , But I could not understand how to use them
Koolman
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How many triangles are there in this figure?

How many triangles are there in this figure? And is there a formula? I found: ABC-ABD-ABG-AFG-ACD-ACG-AEG BCF-BCG-BDG CDG-CEG That is, a total of 12. But not sure if I am missing some.
Tobias Witte
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On a coordinate plane you are given three vertices and trying to find the area.

If the triangle given has the slope of 0 between AB then how would you solve the problem. We are trying to find the area. ex.) A=(0,0) B=(12,0) c=(6,8)
Talib Memon
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Geometry Triangle Problem

Does anyone have a way to do the below without the Angle Bisector Theorem? In △ABC, ∠ABC is 90°. Line segments AB and AC have lengths 6 and 10 respectively. D is a point on BC such that AD bisects ∠CAB. Let E be the foot of the perpendicular from D…
Arunav MAHESHWARI
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In an equilateral triangle $\triangle ABC$, $AD$ is drawn perpendicular to $BC$ meeting $BC$ in $D$. Prove that $AD^{2} = 3 BD^{2}$.

In an equilateral triangle $\triangle ABC$, $AD$ is drawn perpendicular to $BC$ meeting $BC$ in $D$. Prove that $AD^{2} = 3 BD^{2}$.
GAME BUG
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Question related to triangles.

I am stuck at a question: O is a point in the interior of ∆PQR , then which of the following is true: 1)$(OP+OQ+OR)<1/2(PQ+QR+PR)$ 2)$(OP+OQ+OR)=1/2(PQ+QR+PR)$ 3)$(OP+OQ+OR)>1/2(PQ+QR+PR)$ Please can someone explain me how to do this? Thanks for…
codetalker
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Sin Cos equation help

Can you please help me prove that this equation is true? $$\left(1- \frac{2\tan(x)}{\sin(2x)}\right)^2 = \left(1- \frac{2\tan(x)}{\tan(2x)}\right)^2$$
Hashem
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