Theorem 1: Diagonal of a Parallelogram Divides It into Two Congruent Triangles

Q.

Prove that the diagonals of a rhombus are perpendicular. [3 MARKS]

Q. All rectangles are parallelograms.

1. True
2. False

Q. If the area of the $\Delta$AOD is 12 $c{m}^2$, then find the area of the parallelogram ABCD.

1. $24c{m}^2$
2. $12c{m}^2$
3. $60c{m}^2$
4. $48c{m}^2$

Q. Which of the following is correct for a parallelogram?

1. All sides are equal.
2. Adjacent angles are equal.
3. Diagonals are equal.
4. Adjacent angles are supplementary.

Q. Where is the parallelogram method of vector product.??

Q. Match the following according to the properties of a parallelogram.

1. bisect each other
2. are parallel
3. are supplementary

Q. The diagonals of parallelogram ABCD meets at O. Then
$\Delta COD$ congruent to

1. (\ \Delta COB\)
2. (\ \Delta AOD\)
3. (\ \Delta AOB\)

Q. ABCD is a parallelogram. Then $\Delta ABC\cong$ _____

1. $\Delta DAC$
2. $\Delta ACD$
3. $\Delta CBD$
4. $\Delta ADC$

Q. Diagonal of a parallelogram divides it into two ______

1. congruent triangles.
2. triangles of equal area
3. right angled triangles
4. acute angled triangles.

Q.

Which of the following are the properties of a parallelogram?

1. All of these

2. Opposite sides are equal

3. Opposite angles are equal

4. Diagonals bisect each other

Q. Match the following according to the properties of a parallelogram.

1. bisect each other
2. are parallel
3. are supplementary

Q. Please give me all the theorems of areas of parrallegram and triangles

Q. ABCD is a rectangle of area $40c{m}^2$. If X is any point on AB, what is the area of $\Delta XCD$?

1. $20c{m}^2$
2. $40c{m}^2$
3. $80c{m}^2$
4. $Noneofthese$

Q.

Each diagonal of a parallelogram divides it into two

1. Right triangles

2. Congruent triangles

3. Triangles

4. Equilateral triangles

Q.

Each diagonal of a parallelogram divides it into two

1. Right triangles

2. Congruent triangles

3. Equilateral triangles

4. Triangles

Q. Which of the following is correct for a parallelogram?

1. Adjacent angles are supplementary.
2. Diagonals are equal.
3. Adjacent angles are equal.
4. All sides are equal.

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

Q. ABCD is a parallelogram. If AO = 10, OC = 3x + 4, BO = 8, OD = 2y + 2, then find the value of x and y.

1. x = 2, y = 3
2. x = 3, y = 2
3. x = 4, y = 1
4. x = 1, y = 4

Q. Match the following according to the properties of a parallelogram.

1. bisect each other
2. are parallel
3. are supplementary

Q. Choose the correct options:

1. Diagonals in a parallelogram are equal.
2. Diagonals in a parallelogram bisect each other.
3. A diagonal in a parallelogram divides it into two congruent triangles.
4. A parallelogram has 4 diagonals.

Q. Which of the following is correct for a parallelogram?

1. Diagonals are equal.
2. Adjacent angles are supplementary.
3. Adjacent angles are equal.
4. All sides are equal.

Q. Match the following according to the properties of a parallelogram.

1. are parallel
2. are supplementary
3. bisect each other

Q.

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

1. True

2. False

Q. If the diagonals of a quadrilateral ABCD bisect each other at the point O then the quadrilateral ABCD can be a _____.

1. Trapezium
2. Kite
3. Parallelogram
4. None of the above