Question

Fie MNPQ un trapez,MN║PQ,MN=25 cm,iar PQ=10 cm.Stiind ca MP∩NQ={O},iar MP=35 cm si NQ= 42 cm ,calculati lungimile segmentelor OM,ON,OP si OQ.

Answer 1

Δ QOP asemenea cu ΔMON
m(∡QPO)=m(∡OMN)
m(∡PQO)=m(∡ONM)
m(∡QOP)=m(∡MON) opuse la varf

OM/OP=ON/OQ=MN/QP
OM/OP=ON/OQ=25/10=5/2
(35-OP)/OP=5/2      70-2OP=5OP    7OP=70   OP=10      OM=35-10=25
(42-OQ)/OQ=5/2      84-2OQ=5OQ    7OQ=84  OQ=12      ON=42-12=30