RD Chapter 14- Quadrilaterals Ex-14.1 |
RD Chapter 14- Quadrilaterals Ex-14.3 |
RD Chapter 14- Quadrilaterals Ex-14.4 |
RD Chapter 14- Quadrilaterals Ex-VSAQS |

**Answer
1** :
It is given that the two opposite angles of a parallelogram are and .

We know that the opposite anglesof a parallelogram are equal.

Therefore,

…… (i)

Thus, the given angles become

Also,

Therefore the sum of consecutiveinterior angles must be supplementary.

That is;

Sinceopposite angles of a parallelogram are equal.

Therefore,.

And

Hence thefour angles of the parallelogram are , , and .

**Answer
2** :

Let one of the angle of the parallelogram as

Then the adjacent angle becomes

We know that the sum of adjacent angles of the parallelogram is supplementary.

Therefore,

Thus, the angle adjacent to

Since,opposite angles of a parallelogram are equal.

Therefore,the four angles in sequence are ,,and.

**Answer
3** :

Let the smallest angle of the parallelogram be

Therefore, according to the given statement other angle becomes .

Also, the opposite angles of a parallelogram are equal.

Therefore, the four angles become ,, and .

According to the angle sum property of a quadrilateral:

Thus, the other angle becomes

Hence,the four angles of the parallelogram are , , and .

**Answer
4** :

Let the shorter side of the parallelogram be cm.

The longer side is given as cm.

Perimeter of the parallelogram is given as 22 cm

Therefore,

Hence, the measure of the shorter side is cm.

**Answer
5** :

It is given that ABCD is a parallelogram with

We know that the opposite angles of the parallelogram are equal.

Therefore,

Also, and are adjacent angles, which must be supplementary.

Therefore,

Hence , and .

**Answer
6** :

It is given that ABCD is a parallelogram with

We know that the opposite angles of the parallelogram are equal.

Therefore,

Also, and are adjacent angles, which must be supplementary.

Therefore,

Also, and are opposite angles of a parallelogram.

Therefore,

Hence, the angles of a parallelogram are , , and .

**Answer
7** :

The figure is given as follows:

It is given that ABCD is a parallelogram.

Thus,

Opposite angles of a parallelogram are equal.

Therefore,

Also, we have AP as the bisector of

Therefore,

…… (i)

Similarly,

…… (ii)

We have ,

From (i)

Thus, sides opposite to equal angles are equal.

Similarly,

From (ii)

Thus, sides opposite to equal angles are equal.

Also,

**Answer
8** :

The figure is given as follows:

It is given that ABCD is a parallelogram.

Thus

And are alternate interior opposite angles.

Therefore,

…… (i)

We know that the opposite angles of a parallelogram are equal. Therefore,

Also, we have

Therefore,

…… (ii)

In

By angle sum property of a triangle.

From (i) and (ii),we get:

Hence, the required value for is

And is .

**Answer
9** :

Figure is given as follows:

It is given that ABCD is a parallelogram.

DE and AB when produced meet at F.

We need to prove that

It is given that

Thus, the alternate interior opposite angles must be equal.

In and , we have

(Proved above)

(Given)

(Vertically opposite angles)

Therefore,

(By ASA Congruency )

By corresponding parts of congruent triangles property, we get

DC = BF …… (i)

It is given that ABCD is a parallelogram. Thus, the opposite sides should be equal. Therefore,

…… (ii)

But,

From (i), we get:

From (ii), we get:

Hence proved.

Which of the following statements are true (T) and which are false (F)?

(i) In a parallelogram, the diagonals are equal.

(ii) In a parallelogram, the diagonals bisect each other.

(iii) In a parallelogram, the diagonals intersect each other at right angles.

(iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

(v) If all the angles of a quadrilateral are equal, it is a parallelogram.

(vi) If three sides of a quadrilateral are equal, it is a parallelogram.

(vii) If three angles of a quadrilateral are equal, it is a parallelogram.

(viii) If all the sides of a quadrilateral are equal it is a parallelogram.

**Answer
10** :

(i) Statement: In a parallelogram, the diagonals are equal.

False

(ii) Statement: In a parallelogram, the diagonals bisect each other.

True

(iii) Statement: In a parallelogram, the diagonals intersect each other at right angles.

False

(iv) Statement: In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

False

(v) Statement: If all the angles of a quadrilateral are equal, then it is a parallelogram.

True

(vi) Statement: If three sides of a quadrilateral are equal, then it is not necessarily a parallelogram.

False

(vii) Statement: If three angles of a quadrilateral are equal, then it is no necessarily a parallelogram.

False

(viii) Statement: If all sides of a quadrilateral are equal, then it is a parallelogram.

True

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