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

Q.

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

1. True

2. False

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. 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. Given below is a parallelogram. AC and BD are diagonals. If AO = x + y, OC = 5y, DO = 3x, OB = 12, then find x and y.

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

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. 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. 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

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