Question

question 3
1 pts
which of the following statements is false?
all squares are rectangles
all rectangles are squares
all rectangles are parallelograms
all squares are parallelograms
question 4
1 pts
which of the following characteristics do the square and rhombus not have in common?
all sides are congruent
diagonals are perpendicular
diagonals are congruent
diagonals bisect each other

Explanation:

Question 3

• A square has all angles 90° and opposite sides equal, so it's a rectangle (since a rectangle requires 4 right angles and opposite sides equal). So "All squares are rectangles" is true.
• A rectangle has opposite sides equal and 4 right angles, but a square also requires all sides equal. A rectangle can have length ≠ width (e.g., a 2x4 rectangle isn't a square), so "All Rectangles are squares" is false.
• A rectangle has opposite sides parallel and equal (defining a parallelogram), so "all rectangles are parallelograms" is true.
• A square has opposite sides parallel and equal (defining a parallelogram), so "all squares are parallelograms" is true.

• Square: all sides congruent; Rhombus: all sides congruent. So this is a common characteristic.
• Square: diagonals are perpendicular; Rhombus: diagonals are perpendicular. So this is a common characteristic.
• Square: diagonals are congruent (equal in length); Rhombus: diagonals are not necessarily congruent (they bisect each other at right angles but can have different lengths). So this is not a common characteristic.
• Square: diagonals bisect each other; Rhombus: diagonals bisect each other. So this is a common characteristic.

Answer:

B. All Rectangles are squares

Question 4