BM≡MA (ipoteza)
MP≡MP' (ipoteza)⇒( patuilater in care diagonalele se in jumatatersc)
⇒BPAP' paralelogram
mas ∡(MBP)=mas ∡(PBC), BP bisectoare ipoteza
mas ∡(PBC)=mas∡(BPM) alterne interne, MP||BC, BP secanta, ipoteza
⇒ ∡(MBP)=mas∡(BPM)⇒ΔMBPisoscel baza BP⇔MB≡MP
MB≡MP⇒2MB=2MP⇔AB≡PP'⇒BPAP' paralelogram cu diagonalele congruente, BPAP' dreptunghi, cerinta