Question

Please help me

Line RS intersects triangle BCD at two points and is parallel to segment DC.



Which statements are correct? Check all that apply.

△BCD is similar to △BSR.
BR/BD = BS/SC
If the ratio of BR to BD is 2/3 , then it is possible that BS = 6 and BC = 3.
(BR)(SC) = (RD)(BS)
BR/RS = BS/SC

Answer 1

1. △BCD is similar to △BSR.

2. BR/RD = BS/SC

4. (BR)(SC) = (RD)(BS)

Explanation:

Edge 2021

Answer 2

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,

`(BR)/(RD)=(BS)/(SC)`

⇒ B is not true.

3. As we can see BC is greater than BS ,so it cannot possible.

If
`(BR)/(BD)=(2)/(3)` and
`(BR)/(BD)=(BS)/(BC)`

where BS=6 then
`\Rightarrow(2)/(3)=(6)/(BC)\\\Rightarrow\ BC=9`.

4. As RS is parallel to DS then by basic proportionality theorem,

`(BR)/(RD)=(BS)/(SC)`

⇒BR×SC=RD×BS.

5. From 4 its not true that BR/RS = BS/SC.