Question

In a triangle abc x is the midpoint of ac and xy parallel to ab prove y is midpoint

Answer 1

$\textsf{Concept:}$

$\textsf{Basic proportionality theorem(Thales theorem):}$

$\textsf{If a line is drawn parallel to one side of a triangle}$

$\textsf{then it cuts other two sides proportionally.}$

$\textsf{In \triangle\,ABC , by thales theorem, we have}$

$\mathsf{\frac{CX}{AX}=\frac{CY}{BY}}$

$\textsf{Since x is the midpoint of AC, CX=AX}$

$\implies\mathsf{1=\frac{CY}{BY}}$

$\implies\mathsf{CY=BY}$

$\implies\textsf{ Y is the midpoint of BC}$

Answer 2

Step-by-step explanation:

the answwr is above in the image