Question

Which postulate can be used to prove that ABD and CBD are congruent given that BD and AC and BD bisects AC

SAS

SSS

ASA

SSA

Answer 1

SAS

Explanation:

Here we are given two situations:

BD⊥AC

This indicates that angle ADB and CDB are 90 degrees.

Aso we are given that BD bisects AC.

This indicates that AD=DC

So in triangles ADB and CDB , we have

BD=BD (common) (Side)

angle ADB= angle CDB (Angle)

AD=DC (side)

So the two triangles are congruent by SAS congruency.