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Omni-MATH / Six segments S₁,S₂,S₃,S₄,S₅, and S₆ are given in a plane. These are congruent to the edges AB,AC,AD,BC,BD, and CD , respectively, of a tetrahedron ABCD . Show how to construct a se…

Problem

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problem

Six segments S1,S2,S3,S4,S5,S_1, S_2, S_3, S_4, S_5, and S6S_6 are given in a plane. These are congruent to the edges AB,AC,AD,BC,BD,AB, AC, AD, BC, BD, and CDCD , respectively, of a tetrahedron ABCDABCD . Show how to construct a segment congruent to the altitude of the tetrahedron from vertex AA with straight-edge and compasses.
Plain-text mathematical notation (without MathML)
Six segments S₁,S₂,S₃,S₄,S₅, and S₆ are given in a plane. These are congruent to the edges AB,AC,AD,BC,BD, and CD , respectively, of a tetrahedron ABCD . Show how to construct a segment congruent to the altitude of the tetrahedron from vertex A with straight-edge and compasses.
Original LaTeX notation
Six segments $S_1, S_2, S_3, S_4, S_5,$ and $S_6$ are given in a plane. These are congruent to the edges $AB, AC, AD, BC, BD,$ and $CD$ , respectively, of a tetrahedron $ABCD$ . Show how to construct a segment congruent to the altitude of the tetrahedron from vertex $A$ with straight-edge and compasses.

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Source and history

task_id
c53675d0-5eeb-505d-8ab0-1294054188a0
task_key
test--c53675d0-5eeb-505d-8ab0-1294054188a0
task_revision_id
1
config / split
/ test

Official source

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