MATH SOLVE

2 months ago

Q:
# AB ≅ BC and AD ≅ CD What additional information would make it immediately possible to prove that triangles AXB and CXB are congruent using the HL theorem? What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?

Accepted Solution

A:

It is given that, B ≅ BC and AD ≅ CD We need BD perpendicular to AC, then only we can say triangles AXB and CXB are congruent using the HL theorem.
If BD perpendicular to AC, means that AB and CB are the hypotenuse of triangles AXB and CXB respectively.
from the given information ABCD is a square
If BD and AC bisect each other then AX = CXThen only we can immediately possible to prove that triangles AXD and CXD are congruent by SSS congruence theorem