Question

Given: start overline, A, D, end overline, \cong, start overline, B, C, end overline, comma
AD
≅
BC
, start overline, A, B, end overline, \cong, start overline, C, D, end overline
AB
≅
CD
and start overline, C, E, end overline, \cong, start overline, B, E, end overline, .
CE
≅
BE
.

Prove: triangle, F, B, E, \cong, triangle, D, C, E△FBE≅△DCE. find the remaining steps.

Answer 1

I can finish the proof, but I’m missing the definition/position of point F. Where is F located in the figure (e.g. midpoint of AD, intersection of diagonals, on AB, …)? Also is E on segment BC (so CE = BE means E is the midpoint of BC) or just some point equidistant from B and C?

Give the location of F (and whether E lies on BC). If you don’t have the diagram, common completions are:

- If F is the midpoint of AD and E is the midpoint of BC, then AB ≅ CD and AD ≅ BC imply ABCD is a parallelogram, so the midpoints F and E correspond and you can prove △FBE ≅ △DCE by SAS (show FB = DC, BE = CE, and FE = DE using midpoint/parallelogram facts). I can write the full step‑by‑step proof for that case.

- If F is the intersection of the diagonals, there is a different set of equalities (diagonals bisect each other in a parallelogram) and I can show congruence by a different SAS/SSS argument.

Tell me which point F is (or paste the original diagram/text) and I’ll give the remaining steps.