Question

which of the following statements is false?
all squares are rectangles
all squares are parallelograms
all rectangles are parallelograms
all rectangles are squares
question 4
1 pts
which of the following characteristics do the square and rhombus not have in common?
diagonals are perpendicular
all sides are congruent
diagonals bisect each other
diagonals are congruent

Explanation:

First Question (Which of the following statements is false?)

• A square has four right angles and four equal sides, so a rectangle (four right angles, opposite sides equal) includes all squares, so "All squares are rectangles" is true.
• A square has two pairs of parallel sides, so it is a parallelogram (a quadrilateral with two pairs of parallel sides), so "all squares are parallelograms" is true.
• A rectangle has two pairs of parallel sides, so it is a parallelogram, so "all rectangles are parallelograms" is true.
• A rectangle has opposite sides equal, but a square has all sides equal. So there are rectangles (e.g., a rectangle with length 4 and width 3) that are not squares, so "All Rectangles are squares" is false.

• Diagonals are perpendicular: Both square and rhombus have perpendicular diagonals.
• All sides are congruent: Both square (all sides equal) and rhombus (all sides equal) have all sides congruent.
• Diagonals bisect each other: Both square and rhombus (being parallelograms) have diagonals that bisect each other.
• Diagonals are congruent: A square's diagonals are congruent, but a rhombus (unless it's a square) has diagonals of different lengths, so diagonals being congruent is not a common characteristic.

Answer:

D. All Rectangles are squares

Second Question (Which of the following characteristics do the square and rhombus NOT have in common?)