Question

AB and BC are equal and perpendicular to a line segment AB, show that CD bisects AB.

Answer 1

Given

• AB and BC are equal and perpendicular to AB

To prove

• CD bisects AB

Proof

• In ΔAOD and ΔBOC,
• ∠OAD = ∠OBC  (90°)
• ∠AOD = ∠BOC (V.O.A)
• AD = BC (Given)
• ΔAOD ≅ ΔBOC (A.A.S)
• AO = OB (CPCT)
• ∴ CD bisects AB