Question

In the given figure,SV is the median and SW perpendicular to TU.
Prove that ,
(SU)^2-(ST)^2=2TU×VW

Answer 1

Answer:

SU² - ST² = 2 TU × VW

Step-by-step explanation:

SV is the median

=> TV = UV  = TU/2

SW ⊥ TU

=> ST² = SW² + TW²

=>  ST² = SW² + (TV - VW)²

=> ST² = SW² + (TU/2 - VW)²    Eq1

Similarly

=> SU² = SW² + UW²

=>  SU² = SW² + (TV + VW)²

=> SU² = SW² + (TU/2 + VW)²    Eq1

Eq2 - Eq 1

=> SU² - ST² = (TU/2 + VW)² - (TU/2 - VW)²  

using a² - b² = (a+b)(a-b)

=> SU² - ST² = (TU/2 + VW +TU/2 - VW )(TU/2 + VW -  (TU/2 - VW))

=> SU² - ST² = (TU )(2VW)

=> SU² - ST² = 2 TU × VW

QED

Proved

Answer 2

Answer:

SU^2-ST^2=2TU×VW

Step-by-step explanation:

so it's proved☺️☺️