Math, asked by dnyanobakalme, 7 months ago

in triangle pqr line l is perpendicular bisector of PR and intersect PQ at S prove that PS=SR​

Answers

Answered by smartboy4155
2

Answer:

Given: ΔPQR is right angled triangle where Q is right angle

QS ⊥ PR

QM bisect the ∠PQR

To prove: \frac{PM^2}{MR^2}=\frac{PS}{SR}

MR

2

PM

2

=

SR

PS

In ΔPQR,

QM bisector of ∠PQR

\implies\frac{PM}{MR}=\frac{PQ}{QR}⟹

MR

PM

=

QR

PQ

(Property of angle bisector of a triangle)

\implies\frac{PM^2}{MR^2}=\frac{PQ^2}{QR^2}⟹

MR

2

PM

2

=

QR

2

PQ

2

..............(1)

Again in ΔPQR

QS ⊥ PR ⇒ ΔPQR is similar to ΔPSQ is similar to ΔRSQ

in ΔPSQ and ΔPQR

[tex\frac{PQ}{PR}=\frac{PS}{PQ}[/tex] (both triangles are similar)

PQ^2=PR\times PSPQ

2

=PR×PS .........(2)

Similarly form ΔPSQ and ΔPQR

QR^2=PR\times SRQR

2

=PR×SR ..............(3)

From (1) , (2) & (3)

\frac{PM^2}{MR^2}=\frac{PR\times PS}{PR\times SR}

MR

2

PM

2

=

PR×SR

PR×PS

\frac{PM^2}{MR^2}=\frac{PS}{SR}

MR

2

PM

2

=

SR

PS

Hence Proved

Answered by vickytiwari1994
0

Step-by-step explanation:

yes ps = Sr it's prove because pqr is perpendicular

Similar questions