Question

What is/are the difference between trapezoid and isosceles trapezoid?

• A. In isosceles trapezoid, one pair of opposite lines must be parallel to each other whereas in trapezoid, this is not true.
• B. In isosceles trapezoid, one pair of opposite sides must be equal in length whereas in trapezoid, this is not true.
• C. In isosceles trapezoid, if one interior angle is given then other interior angles can be known whereas in non-isosceles trapezoid, this is not true.

Answer 1

Answer: (B), (C)

In isosceles trapezoid, if one interior angle is given then other interior angles can be known whereas in non-isosceles trapezoid, this is not true.

For a quadrilateral to be a trapezoid, the only criteria is that only one pair of opposite sides must be parallel to each other.

Example: PQRS is an trapezoid.
Here $PQ\parallel RS$ and $PS\ne QR,PQ\ne SR$$

Whereas for an isosceles trapezoid, one pair of opposite sides is parallel to each other, and the pair of non-parallel side are equal in measure.
Example: ABDC is an isosceles trapezoid.
Here$AC=BD,AB\parallel CD$

Hence, option (a) is wrong, and option (b) is correct.

Let's analyze option (c).
Considering AC as transversal to AB and CD, $\angle A$ and $\angle C$ are supplementary angles.

$\therefore \angle A={180}^o-\angle C$

We know in isosceles trapezoid, when two non-parallel sides are extended to meet at a point, they form an isosceles triangle. Hence, angles associated with larger parallel side i.e. A & B will be equal.

$\therefore \angle B=\angle A={180}^o-\angle C$
and $\angle D={180}^o-\angle B=\angle C$

Hence, all the interior angles can be known in terms of the given angle $\angle C.$
This is not true for non-isoscles trapezoid.

$\therefore$ Option (c) is correct.