In Fig.$9.17.$ $PQRS$ and $ABRS$ are Parallelograms and $X$ is any point on side $BR$. !enter image description hereIn Fig.$9.17$ $PQRS$ and $ABRS$ are parallelograms and $X$ is any point on side $BR$. Show that i)...--prophetes.ai

In Fig.$9.17.$ $PQRS$ and $ABRS$ are Parallelograms and $X$ is any point on side $BR$. !enter image description hereIn Fig.$9.17$ $PQRS$ and $ABRS$ are parallelograms and $X$ is any point on side $BR$. Show that i) $[PQRS]=[ABRS]$ ii)$[AXS]=1/2\cdot [PQRS]$ I have no clue.

Maybe someone else can help with part (ii), but here's a hint for part (i):

Express the two areas you need to equate in terms of (1) the area of triangles $PAS$, (2) the area of triangle $QRS$, and (3) the area of parallelogram $AQRS$. Notice what has to be true for the areas to be equal, and prove that.