Question

In the figure PS/SQ=PT/TR and PST = angle PRQ. prove that PQR is an isosceles triangle​

Answer 1

given series is 0.7 + 0.77 + 0.777 + ......... to nth term

therefore ,

$S_n$ = 7×(0.1 + 0.11 + 0.111 +......to nth term)

=7/9 ( 0.9 + 0.99 + 0.999 + ...... to nth term )

=7/9 ( 9/10 + 99/100 + 999/1000 + ..... to nth term )

= 7/9 { ( 1 - 1/10 ) + ( 1 - 1/100 ) + ( 1 - 1/1000 ) + .... to nth term }

= 7/9 { 1+1+1+....to nth term } - { 1/10 + 1/100 + 1/1000 +.... to nth term}

= 7/9 { n - 1/10 ( 1 - 1/10 ) ^n / 1 - 1/10 }

= 7/9 { n - 1 ( 1 - 1/10 )^n / 9 }

= 7/9 { n - ( 1 - 1/10 )^n / 9 }

plzz attach figure or diagram

Answer 2

Answer :-

1. Given ps/sq=pt/tr

angle PST = angle PRQ

1. To prove - PQ = PR
2. Proof :- PS/SQ = PT/TR ( Given)
3. PS/SQ+1 = PT/TR+1 ( we adding 1 both side)
4. PS+SQ/SQ = PT+TR/TR
5. PQ/SQ = PR/TR (WE KNOW PS/SQ=PT/TR)
6. PQ=PR
7. If a triangle both sides are equal then triangle is called isosceles triangle.
8. hence proved.............