Răspuns:
Ip. m(∡RPS)=m(∡TSP) => ∡RPS ≡ ∡TSP
si m(∡RSP)=m(∡TPS) => ∡RSP ≡ ∡TPS
C. [RP]≡[TS]
Dem.
ΔRPS ÷ ΔTSP
∡RPS ≡ ∡TSP
[PS]≡[PS] (lat. comuna) ULU
∡RSP ≡ ∡TPS ==> ΔRPS ≡ ΔTSP => [RP] ≡[TS]
( ptr. a arata congruenta celorlaltor perechi de ∡ -uri
m(∡PRS)= 180°- ( m(∡RPS)+m(∡RSP) ) = 180°-(x+y)
m(∡PTS)= 180°- ( m(∡TSP)+m(∡TPS) )= 180°-(x+y)
Dar, m(∡RPS)=m(∡TSP)=x
si m(∡RSP)=m(∡TPS)=y
====> m(∡PRS)=m(∡PTS) => ∡PRS≡∡PTS)
