Q.1 A mason has made a concrete slab. He needs it to be rectangular. In what different ways can he make sure that it is rectangular, explain the answer?

Q.3 Can a trapezium have all angles equal? Can it have all sides equal? Explain

In geometry, a trapezium (known as a trapezoid in American English) is defined as a quadrilateral with at least one pair of parallel sides. Let’s explore whether a trapezium can have all angles equal or all sides equal:

Can a Trapezium Have All Angles Equal?

• Sum of Interior Angles: In any quadrilateral, the sum of the interior angles is always 360 degrees.

• Equal Angles: If all four angles are equal, each must be 360°/4=90°

• Implication: A quadrilateral with all angles equal (each being 90 degrees) is a rectangle.

• Conclusion: While a rectangle fits the definition of a trapezium (having at least one pair of parallel sides), in common usage, the term “trapezium” typically refers to a quadrilateral with only one pair of parallel sides. Therefore, under the traditional definition, a trapezium cannot have all angles equal.

Can a Trapezium Have All Sides Equal?

• Equal Sides: A quadrilateral with all sides equal is a rhombus.

• Angles in a Rhombus: In a rhombus, opposite angles are equal, but they are not necessarily 90 degrees.

• Parallel Sides: A rhombus has two pairs of parallel sides, making it a special type of parallelogram.

• Conclusion: Since a rhombus has two pairs of parallel sides, it does not fit the traditional definition of a trapezium, which has only one pair of parallel sides. Therefore, a trapezium cannot have all sides equal.

In summary, under the standard definitions:

• A trapezium cannot have all angles equal.

• A trapezium cannot have all sides equal.

These conclusions align with the properties of quadrilaterals as outlined in geometry.