Question: Activity
Always, Sometimes, or Never?
Directions: Write ALWAYS, SOMETIMES, or NEVER for each statement.
1. A square is a rectangle. _____
2. A rectangle is a square. _____
3. A rhombus is a parallelogram. _____
4. A parallelogram is a rhombus. _____
5. A trapezoid is a parallelogram. _____
6. A quadrilateral has four sides. _____
7. A rhombus has four right angles. _____
8. A rectangle has four congruent sides. _____
9. An isosceles trapezoid is a trapezoid. _____
10. A square is a parallelogram. _____
11. A kite is a trapezium. _____
12. A trapezium is a kite. _____
1. A square is a rectangle.
- A rectangle is defined as a quadrilateral with four right angles.
- A square has four right angles and all sides equal.
- Therefore, every square meets the definition of a rectangle.
- Answer: ALWAYS
2. A rectangle is a square.
- A rectangle has four right angles but does not require all sides to be equal.
- A square requires all sides equal.
- So, not all rectangles are squares.
- Answer: SOMETIMES (only if all sides are equal)
3. A rhombus is a parallelogram.
- A rhombus is a quadrilateral with all sides equal and opposite sides parallel.
- Parallelogram is a quadrilateral with opposite sides parallel.
- Every rhombus is a parallelogram.
- Answer: ALWAYS
4. A parallelogram is a rhombus.
- Parallelograms do not require all sides equal.
- Rhombus requires all sides equal.
- So, not all parallelograms are rhombuses.
- Answer: SOMETIMES (only if all sides equal)
5. A trapezoid is a parallelogram.
- A trapezoid has exactly one pair of parallel sides.
- A parallelogram has two pairs of parallel sides.
- So, a trapezoid is never a parallelogram.
- Answer: NEVER
6. A quadrilateral has four sides.
- By definition, a quadrilateral has four sides.
- Answer: ALWAYS
7. A rhombus has four right angles.
- A rhombus does not require right angles.
- Only a square (a special rhombus) has four right angles.
- Answer: SOMETIMES
8. A rectangle has four congruent sides.
- Rectangles require right angles but not equal sides.
- Only squares have four congruent sides.
- Answer: SOMETIMES
9. An isosceles trapezoid is a trapezoid.
- By definition, an isosceles trapezoid is a trapezoid with legs equal.
- Answer: ALWAYS
10. A square is a parallelogram.
- A square has two pairs of parallel sides.
- So, it is a parallelogram.
- Answer: ALWAYS
11. A kite is a trapezium.
- A kite has two pairs of adjacent equal sides.
- A trapezium (UK) or trapezoid (US) has at least one pair of parallel sides.
- Kites do not necessarily have parallel sides.
- Answer: SOMETIMES (if kite has parallel sides, rare)
12. A trapezium is a kite.
- A trapezium has at least one pair of parallel sides.
- A kite has two pairs of adjacent equal sides.
- These are different properties.
- Answer: SOMETIMES (only if it meets kite properties)