Theorem 3: Opposite Angles in a Parallelogram Are Equal

Q. The consecutive angles of a parallelogram are ____.

1. equal
2. complementary
3. supplementary
4. None of these

Q.
If the perimeter of the parallelogram ABCD is 20 cm and the length of AB = 6 cm, then what is the length of AD?

1. 4 cm
2. 5 cm
3. 6 cm
4. 7 cm

Q. If one of the angles of a parallelogram is 80°, its opposite angle is ___ degrees.

1. ${80}^{\circ }$
2. ${100}^{\circ }$
3. ${70}^{\circ }$
4. ${60}^{\circ }$

Q.

Consecutive angles of a parallelogram are complementary.

1. True
2. False

Q.

The given figure shows a parallelogram ABCD such that AB = 15 cm, BC = 12 cm, and CN = 10 cm.

What is the length of AM?

1. 7.5 cm

2. 8 cm

3. 9.6 cm

4. 10 cm

Q. We get a rhombus by joining the mid-points of the sides of a

(a) parallelogram

(b) rhombus

(c) rectangle

(d) triangle

Q.

Diagonal $AC$ of a parallelogram $ABCD$ bisects $\angle A$ (see the given figure). Show that

(i) It bisects $\angle C$ also.

(ii) $ABCD$ is a rhombus.

Q. A parallelogram ABCD with diagonals AC = 12 cm and BD = 16 cm is given. What is the length of AD if the perimeter of triangle AOD is 25 cm?

Q. Find the value of $x$ if PQRS is a paralleogram.

1. 1 cm
2. 2 cm
3. 4 cm
4. 3 cm

Q.

In the given figure, if parallelogram ABCD and rectangle ABEF are of equal area then:

1. Perimeter of ABCD < perimeter of ABEF

2. Perimeter of ABCD = ¹/₂ (perimeter of ABEF)

3. Perimeter of ABCD = perimeter of ABEF

4. Perimeter of ABCD > perimeter of ABEF

Q. In figure ABCD is a parallelogram AB​​​​​ is perpendicular to CD&CFperpendicular to AB if AB=8cm & CF=10cm find AD.
with figure

Q. If AB = 5 cm and $\angle A={80}^{\circ }$, then what is the value of $\angle D$?

1. $\angle D={180}^{\circ }$
2. $\angle D={100}^{\circ }$
3. $\angle D={70}^{\circ }$
4. $\angle D={80}^{\circ }$

Q.

The three angles of a quadrilateral are ${75}^{\circ }$, ${90}^{\circ }$ and ${75}^{\circ }$. What is the fouth angle?

1. ${75}^{\circ }$
2. ${150}^{\circ }$
3. ${120}^{\circ }$
4. ${90}^{\circ }$

Q.

In the below-shown figure if AP=BP, AQ=BQ, then can we say that APBQ forms a kite. State true/False.

1. False

2. True

Q.

$\text{In the given figure, ABCD is a}\text{parallelogram. From the given options,}\text{select the values of x}$

1. ${65}^{\circ }$
2. ${75}^{\circ }$
3. ${45}^{\circ }$
4. ${55}^{\circ }$

Q. Find the value of $x$, if ABCD is a parallelogram.

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

Q. If the ratio of the sides of the paralleogram is 3:4 and the perimeter is 28 cm, then find the length of the shorter side of the parallelogram.

1. 8 cm
2. 10 cm
3. 3 cm
4. 6 cm

Q. State True or False.
Daigonals of Parallelogram are bisecet each other.

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

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

Q.

Opposite angles of a parallelogram are ____ .

1. Equal
2. Supplemantary
3. Complementary
4. Unequal

Q. In figure 5.55 $\square$PQRS is a parallelogram, in which A is mid-point of side SR and point B is a point on diagonal PR. such that RB = $\frac{1}{4}$PR. Also, AB when produced meets QR at C. Prove that, point C is mid-point of side QR.

Q. In a parallelogram ABCD, if AB=2x+5, CD=y+1, AD=y+5 and BC=3x-4 then the ratio of AB:BC is

1. 71:21
2. 12:11
3. 31:35
4. 4:7

Q.

If BDEF and FDCE are parallelograms, then point ___ lies equidistant to points B and C.

1. A
2. D
3. F
4. E

Q. Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus.

Q. In $∆$CBS, seg BC $\cong$ seg SC ray CE bisects $\angle$DCS.
ray SE || ray BC. Prove that $\square$ CBSE is a parallelogram (see fig. 5.6)

Q.

If one of the angles of a parallelogram is 80°, its opposite angle is ___degrees.

Q. Any cyclic parallelogram is a

1. rhombus
2. trapezium
3. rectangle
4. square

Q. Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a square is a square.

Q.

In the given figure, ABCD is a quadrilateral whose diagonals intersect at right angles. Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides is a rectangle.