Question

Identify whether each statement is always, sometimes, or never true.

A trapezoid has one pair of parallel sides.
The diagonals of a rhombus are congruent.
A square has four right angles.
A parallelogram has four congruent sides.

1. Always true
2. Sometimes true
3. Never true

Answer 1

In mathematics, certain statements about geometric figures have set truth values based on their definitions: trapezoids always have one pair of parallel sides, the diagonals of a rhombus are congruent only when it's a square, a square always has four right angles, and a parallelogram has four congruent sides only when it's a rhombus or square.

Step-by-step explanation:

The subject of this question is to determine the truthfulness of certain statements regarding geometric figures in mathematics. It's crucial because such distinctions are fundamental in understanding the properties and characteristics of different geometric shapes. Just as we rely on certain postulates and truths within mathematics, like the Pythagorean Theorem in trigonometry, we seek to apply a similar certainty to these statements about trapezoids, rhombi, squares, and parallelograms.

1. A trapezoid has one pair of parallel sides. - Always true.
2. The diagonals of a rhombus are congruent. - Sometimes true (The diagonals of a rhombus are perpendicular bisectors of each other and are congruent only when the rhombus is a square).
3. A square has four right angles. - Always true.
4. A parallelogram has four congruent sides. - Sometimes true (This is true only when the parallelogram is also a rhombus or a square).