# Tagged Questions

For questions about properties and applications of triangles

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### What is the symbol to denote that two triangles are similar?

Does there exist a unique symbol to denote that two triangles are similar to each other without resorting to using the phrase "is similar"?
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### What can be said about triangle with certain condition?

This question comes from 1988 Irish Mathematical Olympiad, for all those interested. A mathematical moron is given the values $b,c,\alpha$ for a triangle $ABC$ and is required to find $a$. He does ...
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### Given a single point in 3d space, and 3 points that make up a triangle, find the closest point in/on the triangle to the point.

Given point $(p,q,r)$ and 3 points which make up a triangle, find the closest point in the triangle to the point in space. From the triangle, we can find the equation of the plane $Ax+By+Cz+d=0.$ ...
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### Finding maximum subset-triangles

To a given base (ab), triangles are constructed by choosing a point (p). How can i find the maximum subset-triangles(*)? (*)subset-triangle: p' is inside the triangle abp. Allowed interceptions from ...
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### Why can't the nth triangular number be expressed as the area of an equilateral triangle?

It should be self-intuitive that the $nth$ triangular number is an equilateral triangle with base $n$, and thus its area should equal the value of the triangular number. So, I was wondering: why doesn'...
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### A triangle has sides $2n, n^2+1$ and $n^2-1$ prove that it is right angled

I've tried using Pythagoras theorem but it always results in a silly answer like $n=n^2$ or something. I'm nearly 100% sure this is done with Pythagoras but I'm not sure which way to do it
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### Parallelogram inside of a triangle dependencies

APMH is a parallelogram inside the triangle ABC. It has a perimeter of 18cm. So my question is could MP divide AB by 2 equal parts AP and PB???
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### Prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third and half as long

The task is to prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long. (Or in vector notation PQ = AB / 2). It should be proved ...
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### Given verticies find the area of the triangle formed

When I looked at this problem I didn't think it seemed all that hard until I actually tried it. The problem is this: Given the rectangular vertices $O(0, 0, 0), P(-1, 2, -3), Q(-2, 3, -4), R(0, 0, 1)$...
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### How to work out the angle of a line passing through a plane

I have a triangular plane composed of three points. From this it it easy to deduce that the plane is in fact composed of two vectors which must touch at some point. because all of this is relative, ...
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### Calculus made easy Exercise 9 Question 4 (Doubt)

A piece of string 30 inches long has its two ends joined together and is stretched by 3 pegs so as to form a triangle. What is the largest triangular area that can be enclosed by the string? I took P ...
Here is the problem: Let $A$ be the point with coordinates $(1, 0)$ in $\mathbb R ^2$. Another point $B$ is chosen randomly over the unit circle. What is then the expected value of the area of the ...