Properties of Diagonal of a Parallelogram

Q. $E$ and $F$ are points on diagonal $AC$ of parallelogram $ABCD$, such that, $AE$ = $CF$. We can conclude that, $BFDE$ is a ____.

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

Q.

A diagonal of a parallelogram divides it into two congruent triangles.

1. True

2. False

Q.

If the diagonals bisect each other in a quadrilateral, then, it is a parallelogram.

1. False

2. True

Q. ___ is a quadrilateral whose diagonals are not equal but bisect each other at right angle.

1. Square
2. Rhombus
3. Trapezium
4. Rectangle

Q. Match List – I with List – II and select the correct answer using the codes given below the lists:

$\begin{array}{cc}\text{Properties}& \text{Quadrilaterals}\\ \text{In a parallelogram ABCD}& \\ \text{If}\angle D={115}^{\circ }\text{, then the measure of}\angle A\text{=}& {68}^{\circ }\\ \text{PQRS is a square such that PR and SQ intersect at O}& \\ \text{then the measure of}\angle POQ=& {58}^{\circ }\\ \text{The diagonals of a rectangle ABCD meet at O. If}\angle BOC={44}^{\circ }\text{,}& \\ \text{then the measure of}\angle OAD\text{=}& {90}^{\circ }\\ \text{If ABCD is a rectangle with}\angle BAC={32}^{\circ }\text{, then the measure of}& \\ \angle DBC\text{is =}& {65}^{\circ }\end{array}$
Choose the correct option:

1. $\left(A\right)\to p;\left(B\right)\to q;\left(C\right)\to r;\left(D\right)\to s$
2. $\left(A\right)\to s;\left(B\right)\to r;\left(C\right)\to q;\left(D\right)\to p$
3. $\left(A\right)\to s;\left(B\right)\to r;\left(C\right)\to p;\left(D\right)\to q$
4. $\left(A\right)\to r;\left(B\right)\to s;\left(C\right)\to q;\left(D\right)\to p$

Q. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

1. False
2. True

Q. If the diagonals of a parallelogram are equal and don't intersect at right angles, then it is called a.

1. rhombus
2. rectangle
3. kite
4. Square

Q.

Assertion : If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Reason : The opposite angles of a parallelogram are equal.
Which of the following is correct?

1. A is false and R is true.
2. Both A and R are true and R is the correct explanation of A.
3. Both A and R are true and R is not the correct explanation of A.
4. A is true and R is false.

Q. In a parallelogram ABCD diagonals AC and BD intersects at O and AC =12.8 cm and BD=7.6 cm, then the measure of OC and OD respectively equal to

1. 3.8 cm and 3.2 cm
2. 3.8 cm, 3.8 cm
3. 6.4 cm and 3.8 cm
4. 1.9 cm and 6.4 cm

Q. Given below is a parallelogram ABCD. Find the value of x and y.

1. 4 cm, 6 cm
2. 2 cm, 4 cm
3. 1 cm, 2 cm
4. 3 cm, 4 cm