Given a particular triangle that has been constructed, I want to prove that one of the angles must be $> 45$ degrees.
62826
The concurrence of angle bisector, median, and altitude in an acute triangle
93599
General Proof for the triangle inequality
94091
In $ \triangle ABC$ show that $ 1 \lt \cos A + \cos B + \cos C \le \frac 32$
141496
Could someone make the proof into a hinted exercise?
135365
If $x, y, z$ are the side lengths of a triangle, prove that $x^2 + y^2 + z^2 < 2(xy + yz + xz)$
40952
Showing that sum of angles of hyperbolic triangle is strictly less than $\pi$
23979
Inequality involving sides of a triangle
17459
Determining if an arbitrary point lies inside a triangle defined by three points?
52017
How to Bend profiled rectangle exactly to 45 degrees?
129161
The minimum perimeter and maximum height of a triangle under constraints
87206
Prove that a triangle can be inscribed in the hyperbola $xy=c^2$ whose sides touch the parabola $y^2=4ax$.
143584
Trigonometric ratios for angles greater than $90^\circ$?
62126
Constructing a triangle given 2 sides and the inscribed circle's radius
48339
A triangle with vertices on the sides of a square, with one at a midpoint, cannot be equilateral
72882
If $a$, $b$, and $c$ are sides of a triangle, then $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$.
123133
If, in a triangle, $\cos(A) + \cos(B) + 2\cos(C) = 2$ prove that the sides of the triangle are in AP
127004
Extreme of $\cos A\cos B\cos C$ in a triangle without calculus.