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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why do similar triangles have proportional sides?

I have seen multiple sites where it is proved that the ratio of corresponding sides of two similar triangles is constant. But the thing is they have used trigonometry in that case. As far as I know, trigonometry is itself based on the fact that the…
vighnesh153
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How to find radius of circle through similar triangles?

If PR $= 15$cm and AC $= 5$cm, use similar triangles to find the radius of the circle. I understand how to do similar triangles,but an unsure of how to find the appropriate lengths in order to find the radius. I tried to use my triangle rules to no…
danielmason
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Ratio of radius of two circles in a triangle

Given a triangle with two circles and apex angle equals $\theta$. Find the ratio of radius of the two circles in terms of $\theta$. My approach: treat the circles as incircle and excircle by drawing a line parallel to base. We know that $$…
George carlin
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The Similar Triangles point.

Any scalene triangle can be dissected into 4 similar but non-congruent triangles in three ways, each with a single pair of congruent triangles. Lines connecting the opposing vertices of these congruent triangles happen to concur at a point. Which…
Ed Pegg
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Given $\frac{1}{AH^{2}}=\frac{1}{AB^{2}}+\frac{1}{AC^2}$, prove $AH$ is perpendicular to $BC$

In the right triangle $\triangle$ABC at A with H $\in$ BC that: $$\frac{1}{AH^{2}}=\frac{1}{AB^{2}}+\frac{1}{AC^{2}},$$ prove that AH $\perp$ BC. My idea is to draw AH' $\perp$ BC (H' $\in$ BC) and prove H $\equiv$ H' $$AH' \perp BC \implies…
William Phoenix
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How is this angle relation true?

Either I'm silly and I'm missing something very simple, or my text book is incorrect. I'm trying to verify a line in the text book which claims that sin(a) = s/r. I can't seem to prove this to myself and its infuriating.
QEntanglement
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Whats the sum of the length of all the sides of a triangle?

You are given triangles with integer sides and one angle fixed at 120 degrees. If the length of the longest side is 28 and product of the remaining to sides is 240, what is the sum of all sides of the triangle? I have tried to solve it using the…
Meherzad
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A triangle with integer co ordinates and integer sides

Is there a triangle with integer sides as well as integer co ordinates when none of the angles is $90$? I tried to solve the general case but I am stuck with it. Update: Let the Triangle be $T$ whose vertics are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ such…
HashimKhan
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Why is $ab = cd$ in this triangle?

I'm trying to understand the proof of the reciprocal Pythagorean theorem, but it seems to depend on the fact that $ab = cd$ in the picture above, but I cannot see why. Assuming the result, I can then apply Pythagoras getting $a^2 + b^2 = c^2$…
user1145880
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Problem with triangles and lots on unknown

This problem feel more complicated to me than usual. I am currently stuck with finding some values in the following case. Here the image illustrate the basic of the problem. What the rules are : A and B are always on the orange axis AB,DE and CE…
Franck
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Prove that every primitive triangle has area $1/2$

I am studying triangles on the plane $\mathbb R^2$ whose vertices have integer coordinates. If any such solid triangle (i.e., the convex hull of the vertices) has no other points with integer coordinates, we call it a primitive triangle. I want to…
JoséS09
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Started "doing" Pythagorean theorem problems with isosceles triangles today ...

Yesterday, I solved my very first Pythagorean theorem problem! Everything was going good so far, I was solving harder problems very easily. However, today's lesson is a little bit different. I am working with isosceles triangles, and I have the…
Plamen Dobrev
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If an angle of a triangle is equal to another angle of a triangle, then are the sides opposite the equal sides equal?

In the figure, in between triangles $ABD$ and $ADC$ the angles $BAD$ and $DAC$ are equal. So are the opposite sides equal i.e. $BD = CD$?
tryingtobeastoic
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Solution for the value of angle $A$ of a triangle

In triangle $\triangle \; ABC$ , if $$2\frac{\cos A}{a} + \frac{\cos B}{b} + 2\frac{\cos C}{c} = \frac{a}{bc} + \frac{b}{ca}$$ find angle $A$. This is a quiz bee problem sent to me by my friend in FB. He asked me if I can do a solution for it. …
Romel
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