Answer: A and D are the correct statements.
1. In ΔBRS and ΔBDC
∠R=∠D and ∠S=∠C [∵ corresponding angles]
So by AA similarity criteria ,
△BCD is similar to △BSR.
2. As RS is parallel to DS then by basic proportionality theorem,
[tex]\frac{BR}{RD}=\frac{BS}{SC}[/tex]
⇒ B is not true.
3. As we can see BC is greater than BS ,so it cannot possible.
If [tex]\frac{BR}{BD}=\frac{2}{3}[/tex] and [tex]\frac{BR}{BD}=\frac{BS}{BC}[/tex]
where BS=6 then [tex]\Rightarrow\frac{2}{3}=\frac{6}{BC}\\\Rightarrow\ BC=9[/tex].
4. As RS is parallel to DS then by basic proportionality theorem,
[tex]\frac{BR}{RD}=\frac{BS}{SC}[/tex]
⇒BR×SC=RD×BS.
5. From 4 its not true that BR/RS = BS/SC.
