Question

State true or false:

With reference to the figure,

$R$ is mid-point of $BC$.

• A. True
• B. False

Answer 1

The correct option is A True

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, $△BDC\sim △BOR$ bt AAA
Thus, $\frac{BD}{OB}=\frac{BC}{BR}$
$2=\frac{BC}{BR}$ (O is the mid point of BD)
$BR=\frac{1}{2}BC$
Hence, R is the mid point BC