Question

S and U are two points on side PQ of triangle PQR, such that QU=PS. if ST || QR and UV || PR, then prove that TV || PQ ​

Answer 1

Hence Proved.

Step-by-step explanation:

Given,

$S$ and $U$ are two points on side $PQ$ of $\triangle PQR$ such that $QU=PS$ and if $ST\parallel QR$ and $UV\parallel PR$ then prove that $TV\parallel PQ$

From $\triangle PQR$,

$QU=PS$__1 and $ST\parallel QR$,

So,

⇒$\frac{PS}{SQ}=\frac{PT}{TR}$ __2

Also,

$UV\parallel PR$,

⇒$\frac{QU}{UP}=\frac{QV}{VR}$ __3

Now,

$\frac{QU}{UP}=\frac{QU}{US+PS}=\frac{PS}{US+QU}=\frac{PS}{SQ}$ __4

From equation-1,3 and 4 we get,

$\frac{PT}{TR}=\frac{QV}{VR}$

⇒$\frac{TR}{PT}=\frac{VR}{QV}$

∴ $TV\parallel PQ$

Hence Proved.

Answer 2

Answer:

Step-by-step explanation: