Triangle ABD and CBD are congruent by the SAS postulate
Step-by-step explanation:
Step 1 :
Given ,
Segment AC is perpendicular to BD
Segment BD bisects segment AC
To prove the given two triangles are congruent
Step 2 :
Since AC is perpendicular to BD , We have ∠BDA and ∠BDC to be equal to 90 degrees
Also we have AD = DC , because BD bisects AC
BD is a side common to both the triangles and hence is the same
So we have two sides and angle between them (included angle) to be same for both the triangles.
Hence Triangle ABD and CBD are congruent.
