Quadrilateral inside a parallelogram

Q. $ABCD$ is the parallelogram. $P$, $Q$, $R$ and $S$ are the mid points of sides $AB$, $BC$, $CD$ and $AD$. If $\angle A={70}^o$. Find the acute angle of intersection of diagonal of parallelogram $PQRS$.

1. ${110}^o$
2. ${60}^o$
3. ${70}^o$
4. ${65}^o$

Q. $ABCD$ is the parallelogram and $E$, $F$, $G$ and $H$ are the midpoints of sides $AB$, $BC$, $CD$ and $DA$ respectively. $EF=6$ cm and perimeter of $EFGH$ is $18$ cm. Find the length of diagonal $BD$.

1. $3$ cm
2. $6$ cm
3. $9$ cm
4. $12$ cm

Q. Mid-points of all sides of parallelogram are joined in such a way that a quadrilateral is formed. The formed quadrilateral is

1. Parallelogram
2. Trapezium
3. Kite
4. Rhombus

Q. State if the statement is true or false.

• The quadrilateral so formed when the mid points of adjacent sides of parallelogram are joined is rectangle.

1. True
2. False

Q. The length of diagonals of parallelogram are $4$ cm and $6$ cm. Find out the perimeter of Parallelogram which is formed when the mid points of adjacent sides are joined.

1. $5$ cm
2. $10$ cm
3. $15$ cm
4. $20$ cm

Q. If ABCD is a parallelogram, E and F are midpoints of AD and BC respectively. Then quadrilateral DEBF will be ?

1. A parallelogram
2. A trapezium
3. A rhombus
4. A rectangle