Could I have a clue how to start this?
The edges of a tetrahedron meet at a vertex so that a right angle is formed between each pair of edges. Prove that the base triangle cannot be right angled.
Hello, Stuck Man!
Did you make a sketch?
Three edges of a tetrahedron meet at a vertex so that a right angle
is formed between each pair of edges.
Prove that the base triangle cannot be right-angled.
The sides of the three right angles areCode:* * * * c * * * a* *b * * * *e * * * * * * * * * * d
The sides of the base are
We have: .
Suppose the base triangle has a right angle,
. . then we have (for example): .
Substitute: .
And we have: .
. . There is no tetrahedron.
Therefore, the base triangle canNOT be right-angled.