S and U are the two points on the side PQ of Triangle(PQR), such that QU = PS If - Maths - Triangles

Question

S and U are the two points on the side PQ of
Triangle(PQR), such that QU = PS If ST parallel to
QR and UV parallel to PR, then prove that TV parallel to
PQ

Aakash Sharma · Accepted Answer

Given: In Î”PQR PS = QV (1) ST || QR $\Rightarrow \frac{PS}{SQ} = \frac{PT}{TR} (2)$ UV || PR $\Rightarrow \frac{QU}{UP} = \frac{QV}{VR} (3) Now, \frac{QU}{UP} = \frac{QU}{US + PS} = \frac{PS}{US + QU} = \frac{PS}{SQ} (4)$ From (1) (3) and (4) we get $\frac{PT}{TR} = \frac{QV}{VR} \Rightarrow \frac{TR}{PT} = \frac{VR}{QV}$ â‡’ TV || PQ

S and U are the two points on the side PQ of Triangle(PQR), such that QU = PS. If ST parallel to QR and UV parallel to PR, then prove that TV parallel to PQ.