Geometry Practice Test 5

In ΔAOB and ΔBOD
BO = OB (common perpendicular bisector)
AO = OD
∠AOB = ∠BOD = 90°
⇒ ∠AOB = BOD by Rule SAS
⇒ AB = CD by C.P.CT

Similarly, we can prove that AC = CD.
ΔACD and ΔABD
AB = AC and BD = CD
AD = AD
ΔACD ≅ ΔABD by Rule SAS ⇒ ∠C = ∠D
∠C+∠D = 180
∠C = 90° ⇒ ABCD is a square.