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2answers
78 views

Proving that an equilateral triangle in the plane cannot have vertices on integer lattice points

Thanks for the help! I've written a more detailed proof. The hints were great.
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2answers
58 views

Trigonometry and triangle proof

Question: Prove that in an acute angle triangle ABC: $$\tan A\tan B +\tan A \tan C + \tan B \tan C \geq 9$$ I have no idea where to even begin this question. Please help me!
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2answers
105 views

Two parallelograms are equal in area.

I tried this question by constructing a line $PD$ therefore forming two triangles $ADP$ and QDP but couldn't establish the congruency relation between the triangles. My approach was that if I have ...
3
votes
3answers
79 views

How to prove that triangle inscribed in another triangle (were both have one shared side) have lower perimeter?

This question looks really simple, but to my (and my co-workers) frustration we were not able to prove this in any way. I tried all triangle formulas known to me but I feel I'm missing the point, and ...
1
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2answers
71 views

Proof using properties of an isosceles or right-angle triangle

Given a triangle $ABC$ with sides $AB=BC$ and angle$\angle B=100^\circ $, prove that $$a^3 + b^3 = 3a^2b$$ where $a=AB=BC$ and $b=AC$, I have tried to use simultaneously the sine and cosine rules as ...
1
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1answer
60 views

Geometry Proof Triangles

Show that if two of the corresponding angles of two triangles are equal then so is the third. Is there a formal way to prove this? I wanted to just say in one sentence that if two angles are the ...
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2answers
153 views

How to prove point A belongs to line t?

I'm stuck at trying to prove that any point $A$ will belong to line $t$ if and only if segments $AB=AC$, where $B$ and $C$ are symmetrical points to the line $t$ and $M$ is the midpoint of segment ...
1
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0answers
106 views

Proving that the circumcenter is the centroid

Given a triangle and its centroid, we know that the 3 line segments between the centroid and each of the vertices of the triangle divide the triangle into three smaller triangles. Prove that the ...
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0answers
35 views

How to prove this relationship between sides length in the specific triangle? [duplicate]

Possible Duplicate: Proving that $|CA|+|CB|=2|AB|$ in a general $ABC$ triangle When I was exploring a web collection with geometrical problems I found this one: How can I prove that in ...
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0answers
354 views

Euler's Line of a medial triangle

I have the following problem with a comment below on the steps that I took so far. Here is the example: Let triangle ABC be any triangle. The midpoints of the sides in Triangle ABC are labeled $A', ...