query: Prove that the midpoints of a line segment and the mid points of the diagonals of a quadrilateral are concurrent
positive_passages.docid: 145756
positive_passages.text: Collinearity problem (Newton-Gauss line)
negative_passages.docid: 61066
negative_passages.text: Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
negative_passages.docid: 143525
negative_passages.text: line segment joining two centers of circles is perpendicular to line segment joining two intersection point of the circles
negative_passages.docid: 130851
negative_passages.text: Squaring the plane, with consecutive integer squares. And a related arrangement
negative_passages.docid: 138063
negative_passages.text: Why is the Centroid of a Triangle Shared with Its Midpoint Triangle
negative_passages.docid: 88283
negative_passages.text: Proving the length of angle bisector
negative_passages.docid: 84122
negative_passages.text: Convex Quadrilateral Test
negative_passages.docid: 83449
negative_passages.text: Proof with 3D vectors
negative_passages.docid: 129997
negative_passages.text: Unique line in $\mathbb{P}^3$ through a point $p$ and intersecting two disjoint lines
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 49440
negative_passages.text: Prove that the interval $ \ [0,2)$ and $ \ [5,6) \cup [7,8)$ have the same cardinality
negative_passages.docid: 157660
negative_passages.text: proof $a$ ,$b$ and $c$ can be sides of a triangle
negative_passages.docid: 46308
negative_passages.text: Simultaneous diagonlisation of two quadratic forms, one of which is positive definite
negative_passages.docid: 64305
negative_passages.text: Prove two reflections of lines through the origin generate a dihedral group.
negative_passages.docid: 106327
negative_passages.text: Prove, in this figure, that $EFGH$ is a parallelogram
negative_passages.docid: 119195
negative_passages.text: Proving two lines in vector form intersect algebraically
negative_passages.docid: 124425
negative_passages.text: A geometry question: Let $ABCD$ be a convex quadrilateral. Prove that AD is parallel to BC.