Question

jane heard a student say that all squares are rectangles but not all rectangles are squares. she said this did not sound correct. how do you respond? choose the correct answer below. a. the statement is incorrect. all rectangles are squares, but not all squares are rectangles. b. the statement is incorrect. some rectangles are squares and some squares are rectangles. c. the statement is incorrect. no rectangles are squares and no squares are rectangles. d. the statement is correct. a rectangle is a parallelogram with four right angles. a square has four right angles and four equal sides, so a square is a rectangle. a rectangle does not have to have four equal sides.

Explanation:

To determine the correct answer, we analyze the definitions:

• A rectangle is a parallelogram with four right angles (sides don't have to be equal).
• A square is a rectangle with four equal sides (so all squares are rectangles, but not all rectangles have equal sides, hence not all rectangles are squares).
• Option A: Incorrect. All squares are rectangles (since a square meets the rectangle's definition), so the first part ("All rectangles are squares") is wrong.
• Option B: Incorrect. All squares are rectangles (not just "some"), so this is wrong.
• Option C: Incorrect. All squares are rectangles (so "no squares are rectangles" is false).
• Option D: Correct. It accurately explains that a square is a special type of rectangle (since it has four right angles and is a parallelogram), but a rectangle doesn't need four equal sides, so not all rectangles are squares.

Answer:

D. The statement is correct. A rectangle is a parallelogram with four right angles. A square has four right angles and four equal sides, so a square is a rectangle. A rectangle does not have to have four equal sides.