ABCD is a quadrilateral in which AB = 5 cm, CD = 8 cm and the sum of angle A and angle D is 180°. What is the name of this quadrilateral?
(a) Parallelogram
(b) Trapezium
(c) Rhombus
(d) Can not be determined
Solution:
Given, ABCD is a quadrilateral
AB = 5 cm and CD = 8 cm
The sum of angle A and D is 180 degrees.
We have to find the name of the quadrilateral.
From the given options,
(i) A parallelogram will have two pairs of opposite sides.
AB = 5 cm and CD = 8 cm
The opposite sides are not equal.
Therefore, ABCD is not a parallelogram
(ii) A trapezium has two parallel sides and two non parallel sides.
AB and CD are not parallel.
The sum of two opposite angles is equal to 180 degrees.
Given, the sum of angles of A and D is equal to 180 degrees.
Therefore, ABCD is a trapezium.
(iii) A rhombus will have all four sides equal.
AB and CD are not equal.
Therefore, ABCD is not a rhombus.
✦ Try This: In quadrilateral PQRS, ∠P + ∠S = 180°. What special name can be given to the quadrilateral?
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 6
ABCD is a quadrilateral in which AB = 5 cm, CD = 8 cm and the sum of angle A and angle D is 180°. What is the name of this quadrilateral? (a) Parallelogram, (b) Trapezium, (c) Rhombus, (d) Can not be determined
Summary:
ABCD is a quadrilateral in which AB = 5 cm, CD = 8 cm and the sum of angle A and angle D is 180°. Therefore, ABCD is a trapezium.
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