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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Congruent Triangles

Triangle ABC and Triangle DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC.If AD is extended to intersect BC at P,show that (a)Triangle ABD ≈ Triangle ACD (b)Triangle ABP ≈ Triangle ACP (c)AP…
CrispyElf
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How many triangles in the diagram?

I want to count the number of triangle in the following diagram. I have manually counted the no of triangles in the diagram. The no of triangles is 44. Is there any other way to count the no of triangles?
Christopher Marlowe
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getting the inner corner angle

I have four points that make concave quad: now I wanna get the inner angle of the (b) corner in degrees. note: the inner angle is greater than 180 degree.
Heysem Katibi
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Visually prove area = 1/2 (base * height) for scalene triangle.

Please refer to image for explanation.
Dave Kirkby
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Could you help me approach this problem using sine law?

Given that ABC is an isosceles triangle, $[BD]$ is angle bisector, $\angle BDA = 120^\circ$. Evaluate the degree of $\angle A $ Could you help me approach this problem using sine law? Here's my attempt: From the angle bisector theorem, we know…
Hamilton
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Triangle Point stays the same

The Point $C$ of the triangle $ABC$ lies on the perpendicular to $AB$ trough Point $T$. $\alpha$ is the angle $\angle BAC$. Point $D$ lies on a line with the $\angle CBD=\alpha$. The Point $E$ lies on the perpendicular to $AC$ trough $D$. Proof that…
B. Schulz
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Can I get some example coordinates of an equilateral triangle, but only integers?

I'm trying to implement Bresenham's Circle drawing algorithm and I intend to draw a circumscribed and inscribed circle (circumcircle and incircle) in a triangle. I need some simple ways to find coordinates of an equilateral triangle to test my…
Uzumaki Boruto
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Angle between triangle orthocenter, center of inscribed circle and centroid is always obtuse

If $S$ is the center of inscribed circle, $T$ centroid and $H$ orthocenter of a triangle, prove that $\angle TSH$ is always obtuse (i.e. $\gt 90^{\circ}$, with equilateral triangle being the only exception). Or you can put it this way: Prove that…
Saša
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Coordinates of a point on the side of a triangle

I know the coordinates of the $3$ vertices of a triangle and the $y$ coordinate of a fourth point on one side. How do I find the $x$ coordinate of the fourth point? I feel I'm missing something obvious. $$A(0, 0), B(844, 0), C(844, 2000)$$ The…
Jonathan Lackey
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How to find the inverse position inside a triangle

If I were standing in a equilateral triangle - How do I calculate the inverse of my position? Can it be done? It's easy inside a rectangle, but I can't think of how you would do it inside of a triangle. For instance if I'm in one corner of a…
Emery King
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Prove that the perpendicular bisectors of all 3 sides of a triangle intersect in one point

I don't know where to start. Ceva's theorem?
Gerard L.
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Display of cups in triangle/pyramid

In this above picture, there are 15 cups, to make a perfect pyramid, you start the bottom row with 5 cups. What is the formulae to start the bottom row, if I have $n$ cups.
Broken Link
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Two legs of a right triangle have lengths 14 and 9. The mreasure of the smaller acute angle to the nearest degree is

Two legs of a right triangle have lengths 14 and 9. The measure of the smaller acute angle to the nearest degree is....? Can someone talk me through this? I'm literally stressing out and cannot understand what i'm supposed to do? I do not need the…
Danneh Corn
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When does a perpendicular drawn through an angle of a triangle to a line of that same triangle bisect that angle?

Let's assume a right triangle where ∠BAC =90° and a perpendicular has been drawn to hypotenuse "BC" from point "A". And this perpendicular intersects hypotenuse at point "D" such that ∠ADB and ∠ADC equal to 90°. Does this perpendicular bisects…
user64814
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Generating integral triangles with two equal sides

How can I generate all triangles which have integral sides and area, and exactly two of its three sides are equal? For example, a triangle with sides ${5,5,6}$ satisfies these terms.
Khaled
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