MATH SOLVE

4 months ago

Q:
# Please help meLine 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/SCIf 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

Accepted Solution

A:

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.