Question

In the above bridge, line segment BD is the perpendicular bisector of line segment AC. For the bridge to be safe, Triangle ABD is congruent to Triangle CBD. Considering strictly the information that was given, what sequence of reasons can you use to prove that Triangle ABD is congruent to Triangle CBD?

Answer 1

Answer: SAS postulate will be use to prove  Δ ABD ≅ ΔCBD

Step-by-step explanation:

Here, In ΔABC line segment BD is the perpendicular bisector of line segment AC,

Therefore, BD ⊥ AC and, AD=DC

Thus, In triangles ABD and CBD,

AD≅DC     ( given)

∠ADB≅∠CDB ( Right angles)

BD≅BD            ( Reflexive)

Therefore, By SAS postulate of congruence,

Δ ABD ≅ ΔCBD.