A quadrilateral with one pair of parallel side is a A) Parallelogram B) Square C) Rectangle D) Trapezium
Answer
Verified
Hint: In order to solve this question, we must know that quadrilaterals have special properties. Also we have to make figures, this will give us a clear picture of what our approach should be. By understanding the properties of different quadrilaterals will help us in solving this question.
Complete step-by-step answer: Quadrilaterals are a special type of polygon. The meaning of the word “quadrilateral” is “quad” means “four” and “lateral” is derived from the Latin word for “side”.
So a quadrilateral is a four-sided polygon. Let’s start explaining all the options one by one,
(A) Parallelogram –
The quadrilateral with two pairs of parallel sides is called parallelogram. A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal. As,
parallelogram has two pairs of parallel sides. So, option A is incorrect.
(B) Square-
A square is one of the most basic geometric shapes. It is a special case of parallelogram that has four congruent sides and four right angles that is ${90^ \circ }$. As, square has four congruent sides. So option B is
incorrect.
(C) Rectangle-
A rectangle is a parallelogram because its pairs of opposite sides are parallel. A rectangle also has the special characteristic that all of its angles are right angles; all four of its angles are congruent. As, rectangle has 2 pairs of parallel sides. So, the option
C is incorrect.
(D) Trapezium-
A trapezium is a quadrilateral with exactly one pair of parallel sides. One pair of opposite sides being parallel and the other pair not parallel. As, trapezium has exactly one pair of parallel sides. So, the right answer is option D.
Note: Whenever we face such types of
questions, the key concept is that we have to examine all the quadrilaterals one by one given in this question. By examining one by one diagrammatically and theoretically we find out that trapezium is a quadrilateral with one parallel side, By using this approach we will get our answer.
A quadrilateral having one and only one pair of parallel sides is called
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Solution
The correct option is D
Trapezium
A trapezium is a quadrilateral that has only one pair of parallel sides. The other pair of sides are not parallel.
Q.
Complete each of the following statements by means of one of those given in brackets against each: (i) If one pair of opposite sides are equal and parallel, then the figure is ........................ (parallelogram, rectangle, trapezium)
(ii) If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is ................ (square, rectangle, trapezium)
(iii) A line drawn from the mid-point of one side of a triangle .............. another side
intersects the third side at its mid-point. (perpendicular to parallel to, to meet)
(iv) If one angle of a parallelogram is a right angle, then it is necessarily a ................. (rectangle, square, rhombus)
(v) Consecutive angles of a parallelogram are ................... (supplementary, complementary)
(vi) If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ............... (rectangle, parallelogram, rhombus)
(vii) If
opposite angles of a quadrilateral are equal, then it is necessarily a .................... (parallelogram, rhombus, rectangle)
(viii) If consecutive sides of a parallelogram are equal, then it is necessarily a .................. (kite, rhombus, square)
