PQRS is a trapezium SQ is a diagonal E and F are two points on parallel sides PQ - Maths - Triangles

Question

PQRS is a trapezium SQ is a diagonal E and F are two points on
parallel sides PQ and RS respectively LIne joining E and F
intersects SQ at G Prove that SG × QE = QG× SF

Rishabh Mittal · Accepted Answer

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In ∆EQG and ∆FSG∠EQG=∠FSG  Alternate Interior Angles∠QEG=∠SFG  Alternate Interior AnglesSo,By AA Similarity criterion∆EQG≃∆FSGSo,SGQG=SFQESG×QE=SF××QGHence Proved

PQRS is a trapezium. SQ is a diagonal. E and F are two points on parallel sides PQ and RS respectively. LIne joining E and F intersects SQ at G. Prove that SG × QE = QG× SF