NCERT Class 8 Mathematics Solutions: Chapter 3 –Understanding Quadrilaterals Exercise 3.3 Part 3

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Given this figure theorems conditions for parallelograms

Theorems Conditions for Parallelograms

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Question: 3 Can a quadrilateral ABCD be a parallelogram, if:

(i)

(ii) cm, and ?

(iii)

Answer:

(i) Yes,

Quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180° but it should also fulfill some conditions such as:

  • Sum of the adjacent angles should be 180°.

  • Opposite angles must be equal.

Image:

Opposite Angles of a Parallelogram Are Equal

(ii) No

In this case because one pair of opposite sides is equal and another pair of opposite sides are unequal. So, it is not a parallelogram.

Image:

Same Opposite Angle Are Equal in Parallelogram

(iv) No

because, opposite angles are equal in parallelogram and here opposite angles are not equal in quadrilateral ABCD. Therefore it is not a parallelogram.

Image:

Opposite Angles of a Parallelogram is Not Equal

Question: 4 Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures.

Answer:

ABCD is a quadrilateral in which angles

Therefore, it could be a kite.

Image:

Quadrilateral in Which Angles Are Same

Question: 5 The measure of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.

Answer:

Let two adjacent angles be and.

Since the adjacent angles in a parallelogram are supplementary.

Image:

Angles in a Parallelogram Are Supplementary

One angle =

And another angle