Question

If P,Q,R,S are the mid of side AB,BC,CD,andAD proved that line segment PR and QS bisect each other

Answer 1

Answer:

To PR and QS bisect each other, i.e, OP=OQ & OQ=OS

In Triangle PSO and QOR,

PS=OR (opp. sides of a parallelogram)

∠SPO = QRO (alt. int. angles)

∠PSO = ∠QRO (alt. int. angles)

Therefore, △POS ≅ △ROQ (ASA rule)

OS = OQ (cpct)

Similarly △SOR ≅ △QOP

OP = OR

Therefore PR and QS bisect each other.