Chhattisgarh Board Solutions for Exercise 10: Exercise

$ABCD$ is a trapezium where $AB\parallel DC$ . $E$ is the midpoint of $AD$. A line drawn from $E$, parallel to $AB$, meets $BC$ at point $F$. Prove that $F$ is the mid point of $BC$.

$ABCD$ is rhombus and $P, Q, R, S$ are the midpoints of the sides $AB, BC, CD$ and $DA$ respectively. Show that quadrilateral $PQRS$ is a rectangle.

$ABCD$ is a rectangle in which $P, Q, R, S$ are the mid points of sides $AB, BC, CD$ and $DA$ respectively. Show that quadrilateral $PQRS$ is a rhombus.

$ABCD$ is a quadrilateral in which $P$, $Q$, $R$ and $S$ are midpoints of the sides $AB$, $BC$, $CD$ and $DA$. $AC$ is a diagonal. Show that $SR\parallel AC$ and $SR=\frac{1}{2}AC$.

$ABCD$ is a quadrilateral in which $P$, $Q$, $R$ and $S$ are midpoints of the sides $AB$, $BC$, $CD$ and $DA$. $AC$ is a diagonal. Show that $PQ=SR$.

$ABCD$ is a quadrilateral in which $P$, $Q$, $R$ and $S$ are midpoints of the sides $AB$, $BC$, $CD$ and $DA$. $AC$ is a diagonal. Show that $PQRS$ is a parallelogram.