Question

Which statement is true about the given information?

A line has points B, C, D, and E. All points are equal distances from each other.

BD = One-halfBC
BC = One-halfBE
BD ≅ CE
BC ≅ BD

Answer 1

Assuming the points are in order B–C–D–E with equal consecutive spacing (BC = CD = DE):

- BD = BC + CD = 2·BC, so BD = 1/2 BC is false.
- BE = BC + CD + DE = 3·BC, so BC = 1/2 BE is false (BC = 1/3 BE).
- CE = CD + DE = 2·BC, so CE = BD. Therefore BD ≅ CE is true.
- BC ≅ BD is false (BD = 2·BC).

So the true statement is: BD ≅ CE.