Question

In the given figure, $2AP=5PB$ and $2CP=5PD$

Is $:AC||DB$ ?
If the above statement is true then mention answer as 1, else mention 0.

Answer 1

Given, 2 PA = 5 PB and 2 CP = 5 PD

hence, $\frac{PA}{PB}=\frac{5}{2}$ and $\frac{PC}{PD}=\frac{5}{2}$

Now, in $△$PAC and $△$PDB,

$\angle APC=\angle BPD$ (Vertically opposite angles)

$\frac{PA}{PB}=\frac{PC}{PD}$

Thus, $△APC\sim △BPD$ (SAS rule)

hence, $\angle CAP=\angle PBD$ (Corresponding angles of similar triangles)

$\angle ACP=\angle PDB$ (Corresponding angles of similar triangles)

Thus, AC II BD (Alternate angles are equal, thus the lines are parallel)