Question

Answer if its sometimes, always, or never. Ty

1. A square is a rectangle.
2. A rhombus is a square.
3. A parallelogram is a square.
4. A rectangle is a rhombus.
5. A parallelogram is a square.
6. A parallelogram is a rectangle.
7. A quadrilateral is a parallelogram.
8. A square is a rectangle and a rhombus.
9. An equilateral quadrilateral is a rhombus.
10. An equiangular quadrilateral is a rectangle.

Answer 1

In geometry, a square is always a rectangle; a rhombus or rectangle can sometimes be a square; a parallelogram or quadrilateral can be a rectangle or square depending on certain property fulfillment; and an equilateral or equiangular quadrilateral is always a rhombus or rectangle respectively.

Step-by-step explanation:

The discussion about various geometric shapes pertains to the subject of Mathematics, more specifically to the classification of quadrilaterals. Let's address each statement with regard to it being sometimes, always, or never true.

1. A square is always a rectangle because it has all the properties of a rectangle (four right angles and opposite sides that are equal).
2. A rhombus is sometimes a square. It is a square only when all angles are right angles.
3. A parallelogram is sometimes a square if all sides are equal and angles are right angles.
4. A rectangle is sometimes a rhombus. It is a rhombus when all sides are of equal length.
5. This is a repetition; as stated, a parallelogram is sometimes a square.
6. A parallelogram is sometimes a rectangle if all angles are right angles.
7. A quadrilateral is sometimes a parallelogram. It is a parallelogram when opposite sides are parallel.
8. A square is always a rectangle and a rhombus, as it meets the definitions of both.
9. An equilateral quadrilateral is always a rhombus, as 'equilateral' means all sides are equal which defines a rhombus.
10. An equiangular quadrilateral is always a rectangle, as 'equiangular' means all angles are equal and in a quadrilateral, this implies all are right angles.

The distinction among these geometric terms helps us understand and describe the properties and relations of shapes in geometry. This understanding is crucial in many applications of geometry in real-life scenarios such as architecture, engineering, design, and more.