Question

MNPQ -trapez isoscel cu(MQ) congruent cu(QP) congruent(NP) si m(M)=60(grade).Aratati ca MP_|_PN
Va rog sa ma ajutați,am nevoie

Answer 1

Fiind trapez isoscel si stiind ca m(M) = 60 grade
⇒ m(N) = 60 grade
   m(Q) = m(P) = (360 - 60×2) / 2 = 120 grade

Ducem PS _I_ MN
In Δ MPS, dr.in S :
m(N) = 60 grade
m(S) = 90 grade
⇒ m(P ) = 180 - (60+90) = 30 grade

In Δ MPQ, isoscel, deoarece MQ≡QP :
m(Q) = 120 grade
⇒ m(QMP) = m (QPM) =( 180-120 ) / 2 = 30 grade

In Δ MPS, dr. in S :
m(S) = 90 grade
m(M) = 60-30 = 30 grade
⇒m(P) = 180-(90+30) = 60 grade

Pentru a demonstra ca MP _I_PN trebuie sa aratam ca m(MPN) = 90 grade

m(MPN) = m(MPS) + m(SPN) = 60 +30 = 90 grade
⇒ MP _I_ PN