Question

Select all the statements that are true.
Every rectangle has 4 equal sides.
Every rhombus has 4 right angles.
Every parallelogram has two pairs of opposite sides that are parallel and equal in length.
Every square has 4 equal side lengths and 4 equal angles.
Every trapezoid has two pairs of opposite sides that are parallel.

Answer 1

Let's analyze each statement for its truth:

1. **Every rectangle has 4 equal sides.**
- False. A rectangle has opposite sides that are equal in length, but not necessarily all four sides are equal. Only a square is both a rectangle and has 4 equal sides.

2. **Every rhombus has 4 right angles.**
- False. A rhombus has all sides equal, but its angles are not necessarily right angles. A square is a special case of a rhombus that has right angles.

3. **Every parallelogram has two pairs of opposite sides that are parallel and equal in length.**
- True. By definition, a parallelogram has opposite sides that are both equal in length and parallel.

4. **Every square has 4 equal side lengths and 4 equal angles.**
- True. A square is a special case of a rectangle and rhombus with both equal side lengths and equal angles (90 degrees).

5. **Every trapezoid has two pairs of opposite sides that are parallel.**
- False. A trapezoid (in the American sense) typically has only one pair of parallel sides. A quadrilateral with two pairs of parallel sides is called a parallelogram.

Based on this analysis, the true statements are:

- Every parallelogram has two pairs of opposite sides that are parallel and equal in length.
- Every square has 4 equal side lengths and 4 equal angles.