# Important Results Related to Parallelograms

## Trending Questions

**Q.**

X = set of all quadrilaterals. Y = set of all rhombuses.

**Q.**

Area of parallelogram is the product of base and corresponding height.

True

False

**Q.**

Area of parallelogram is the product of base and corresponding height.

Base

- Height

**Q.**The bisectors of any two adjacent angles of a parallelogram intersect at

**Q.**

The given figure represents a parallelogram PQRS in which PM and RN are perpendiculars drawn to the diagonal QS.

If the area of the shaded region is 40 cm2, then what is the area of the parallelogram PQRS?

60 cm

^{2}80 cm

^{2}100 cm

^{2}120 cm

^{2}

**Q.**

Three statements are given below:

I. In a ||gm, the angle bisectors of two adjacent angles enclose a right angle.

II. The angle bisectors of a ||gm form a rectangle.

III. The triangle formed by joining the midpoints of the sides of an isosceles triangle is not necessarily an isosceles triangle.

Which is true?

(a) I only

(b) II only

(c) I and II

(d) II and III

**Q.**

In the above figure, ACDF, ABEF and BCDE are parallelograms. Analyse the given figure and choose the correct option(s).

∠AFE=x

∠FBD=x+y

∠BCD=z

∠CDG=x+y

**Q.**

To determine all the angles of a parallelogram, which of the following is the minimum necessary condition?

Only one angle is known.

Two angles are known.

Three angles are known.

Length of sides should be known

**Q.**PQRS is a rhombus in which altitude from S to side PQ bisects PQ , then prove that perimeter of PQRS is 4 times of QS.

**Q.**

If one angle of a parallelogram is 24∘ less than twice the smallest angle, then the measure of the largest angle of the parallelogram is

102∘

176∘

68∘

112∘

**Q.**PQRS is a parallelogram. If U and V are mid points of PQ and RQ respectively then area of suv with respect to area of pqrs is

**Q.**Find the value of x if PQRS is a parallelogram.

[2 Marks]

**Q.**

**Question 7**

Two parallelograms are on equal bases and between the same parallels the ratio of their areas is:

A) 1:2

B) 1:1

C) 2:1

D) 3:1

**Q.**The adjacent angels of a parallelogram are x∘ and (2x+30)∘. Find the value of x.

- 40∘
- 50∘
- 45∘
- 55∘

**Q.**If measures opposite angles of a parallelogram are (60 − x)° and (3x − 4)°, then find the measures of angles of the parallelogram.

**Q.**

In a rhombus ABCD, if BC = 8.5 cm, then AB = ?

7.5 cm

4.25 cm

17 cm

8.5 cm

**Q.**Two adjacent angles of rhombus are 3x−40∘ and 2x+20∘.Find the measurement of the greater angle.

- 160∘
- 100∘
- 80∘
- 120∘

**Q.**Diagonals of a quadrilateral ABCD bisect each other. If ∠A=35∘, determine ∠B.

**Q.**If area of a || gm with sides a and b is A and that of a rectangle with sides a and b is B, then

(a) A > B

(b) A = B

(c) A < B

(d) A ≥ B

**Q.**A quadrilateral ABCD will be a parallelogram for the following conditions.

∠D+∠B=1800

**Q.**

**Question 2**

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

**Q.**In Q.No. 1, if AD = 6 cm, CF = 10 cm, and AE = 8 cm, find AB.

**Q.**

In the above figure, ACDF, ABEF and BCDE are all parallelograms. Analyse the given figure and chosse the correct option.

Opposite sides are equal.

Opposite angles are equal.

Opposite angles are bisected by the diagonals.

Diagonals bisect each other.

**Q.**If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is

(a) 108°

(b) 54°

(c) 72°

(d) 81°

**Q.**In △ABC and △DEF, AB=DE, AB∥DE, BC=EF and BC∥EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that

(i) Quadrilateral ABED is a parallelogram

(ii) Quadrilateral BEFC is a parallelogram

(ii) AD∥CF and AD=CF

(iv) Quadrilateral ACFD is a parallelogram

(v) AC=DF

(vi) △ABC≅△DEF

**Q.**

Which of the following statements is/are true?

60

^{o}50

^{0}40

^{0}90

^{0}

**Q.**As shown in the figure, a square is drawn sharing one corner with a right triangle and the other three corners on the sides of this triangle. Calculate the length of a side of the square.

**Q.**

The angle-bisectors of a parallelogram form a quadrilateral as shown in the figure. What can be said about the quadrilateral ABCD?

It's a parallelogram with three acute angles

It's a parallelogram with three obtuse angles

It's a parallelogram with each angle equal to 90∘

It's a parallelogram with adjacent sides equal

**Q.**How much paper of each shade is needed to make a kite given in the figure, in which ABCD is a square with diagonal 44 cm?

**Q.**Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)°. Find the angles of the parallelogram.