query: To prove that triangles of side $a^n, b^n, c^n$ are isosceles.
positive_passages.docid: 83788
positive_passages.text: Condition on sides of triangle to proof it is isoceles
negative_passages.docid: 131754
negative_passages.text: Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $?
negative_passages.docid: 36980
negative_passages.text: Prove the third isomorphism theorem
negative_passages.docid: 125868
negative_passages.text: Prove $a \equiv b \pmod{c} \implies a^n \equiv b^n \pmod{c}$.
negative_passages.docid: 10236
negative_passages.text: Show that $a^n \mid b^n$ implies $a \mid b$
negative_passages.docid: 50417
negative_passages.text: Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.
negative_passages.docid: 145662
negative_passages.text: Prove that two lines are perpendicular in isosceles triangle geometrically
negative_passages.docid: 90056
negative_passages.text: A synthetic geometrical proof required on a result regarding Isosceles triangles.
negative_passages.docid: 45702
negative_passages.text: For any triangle with sides $a$, $b$, $c$, show that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge 0$
negative_passages.docid: 109880
negative_passages.text: Prove that the perpendiculars from P,Q,R to BC,CA,AB respectively are also concurrent.
negative_passages.docid: 20110
negative_passages.text: How to prove $(AB)^T=B^T A^T$
negative_passages.docid: 135814
negative_passages.text: Prove certain subsets of $\mathbb R^n$ are subspaces
negative_passages.docid: 21457
negative_passages.text: Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
negative_passages.docid: 27954
negative_passages.text: Prove triangle inequality using the properties of absolute value
negative_passages.docid: 82474
negative_passages.text: Isometries of $\mathbb{R}^n$
negative_passages.docid: 46260
negative_passages.text: Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
negative_passages.docid: 69131
negative_passages.text: Different proofs of $\,a^n-b^n =(a-b)\sum_{i=0}^{n-1} a^i b^{n-1-i} $?