Question

State true or false:

With reference to the figure,

$2PR=AB+AC$.

• A. True
• B. False

Answer 1

The correct option is B False

Consider PR meets BD at O
In $△$, BDC and BOR,
$\angle B=\angle B$ (Common)
$\angle BDC=\angle BOR$ (Corresponding angles of parallel lines)
$\angle BCD=\angle BRO$ (Corresponding angles of parallel lines)
thus, $△BDC\sim △BOR$ by AAA
Thus, $\frac{BD}{OB}=\frac{DC}{OR}$
$2=\frac{DC}{OR}$ (O is the mid point of BD)
$OR=\frac{1}{2}DC$
Similarly, $OP=\frac{1}{2}AB$
Hence, $OR+OP=\frac{1}{2}(AB+DC)$
$2PR=AB+CD$