Answer:
ΔRCQ = ΔAPS
QR = PS (CPCTC)
ΔSRD ≅ ΔQPB
PQ = RS (CPCTC)
Step-by-step explanation:
Given that ABCD is a parallelogram, we have;
AD = BC, and DC = AB (Definition of a parallelogram)
AD = AS + SD Given S is midpoint of AD
Similarly,
DC = DR + RC
BC = BQ + QC
AB = AP + PB
RC = DR = AP = PB
BQ = QC = QC = BQ segments on either sides of midpoint
∠BCA = ∠DAB (opposite interior angles of a parallelogram)
ΔRQC ≅ ΔSPA
ΔRCQ = ΔAPS (Side Angle Side SAS rule of congruency)
Therefore, segment QR = segment PS (QR = PS) (Corresponding Parts of Congruent Triangles are Congruent CPCTC)
Similarly we have;
∠CDA = ∠CBA (opposite interior angles of a parallelogram)
ΔSRD ≅ ΔQPB (opposite interior angles of a parallelogram)
Therefore, segment PQ = segment RS (PQ = RS) (Corresponding Parts of Congruent Triangles are Congruent CPCTC).
