query: Prove that two lines are perpendicular
positive_passages.docid: 143525
positive_passages.text: line segment joining two centers of circles is perpendicular to line segment joining two intersection point of the circles
negative_passages.docid: 65964
negative_passages.text: Prove that the line joining the midpoint of parallel sides of a trapezium passes through the point of intersection of diagonals
negative_passages.docid: 22856
negative_passages.text: Ways to go from A to B(proof)
negative_passages.docid: 90056
negative_passages.text: A synthetic geometrical proof required on a result regarding Isosceles triangles.
negative_passages.docid: 152476
negative_passages.text: Unique Perpendicular Geodesic
negative_passages.docid: 105367
negative_passages.text: Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
negative_passages.docid: 57406
negative_passages.text: Proving the volume of a cone
negative_passages.docid: 55853
negative_passages.text: Proof using Taylor's theorem
negative_passages.docid: 3820
negative_passages.text: Prove that $||x|-|y||\le |x-y|$
negative_passages.docid: 140717
negative_passages.text: Explain why perpendicular lines have negative reciprocal slopes
negative_passages.docid: 149801
negative_passages.text: prove that $TS = ST$
negative_passages.docid: 95379
negative_passages.text: Prove that $V = V_1 \oplus V_2$ in the following
negative_passages.docid: 68700
negative_passages.text: Proving Two Limits Are Equal to Each Other
negative_passages.docid: 119195
negative_passages.text: Proving two lines in vector form intersect algebraically
negative_passages.docid: 65075
negative_passages.text: norm (x+y)= norm(x-y) implies x is perpendicular to y.
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$
negative_passages.docid: 124425
negative_passages.text: A geometry question: Let $ABCD$ be a convex quadrilateral. Prove that AD is parallel to BC.