Diagonals of a Rhombus Bisect the Pairs of Opposite Angles

Q. A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

Q.

If the angle bisector of an angle of a parallelogram passes through the vertex opposite to it, then the parallelogram will be a rhombus.

1. True

2. False

Q. 38. Diagonal AC of a parallelogram ABCD bisects Angle A then show that its bisects angel c also and abcd is a rhombus

Q. ABCD is a rhombus , an altitude is drawn from D on AB bisects AB . then find the angles of the rhombus ?

Q.

Where notations have usual meanings, the quadrilateral in the figure

1. Is definitely a parallelogram

2. May be a rhombus

3. May be a rectangle

4. All of the above

Q. A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

Q.

If the angle bisector of an angle of a parallelogram passes through the vertex opposite to it, then the parallelogram will be a rhombus.​

1. False

2. ar(BAC) = ar (DPQ)

3. True

4. None of these

Q. ABCD is a rhombus. Length of the diagonal BD is half the length of AB. The perimeter of rhombus ABCD is 160 cm. Find the length of BO.

1. 8 cm
2. 5 cm
3. 20 cm
4. 10 cm

Q.

Match the two columns.

Column 1	Column 2
A parallelogram is a rectangle if and only. if its diagonals are...	bisect each other.
The diagonals of a parallelogram.	parallel to the third
The line joining the mid-points of two sides of a triangle is	the third side
The line is drawn through the mid-point of one side of a triangle parallel to the other bisects	equal

Q. In the given figure, ABCD is a square , then the value of 'x' is

1. ${50}^{\circ }$
2. ${40}^{\circ }$
3. ${35}^{\circ }$
4. ${130}^{\circ }$

Q. Which of the following is not the property of a rhombus?

1. Diagonals bisect each other
2. All sides are equal
3. Opposite angles are equal
4. Diagonals are equal

Q.

If the angle bisector of an angle of a parallelogram passes through the vertex opposite to it, then the parallelogram will be a rhombus.

1. True

2. False

Q.

The quadrilateral formed by joining the mid-points of consecutive sides of a rectangle ABCD, taken in order, is a rhombus.

1. PQRS is a rectangle

2. PQRS is a parallelogram

3. diagonals of PQRS are equal and bisect each other

4. diagonals of PQRS are perpendicular and bisect each other