33. Which of the following has exactly four lines of symmetry?
Answer: D
A square has exactly four lines of symmetry.
A square possesses four lines of symmetry, which include two diagonals and two lines that bisect the square horizontally and vertically. These lines divide the square into symmetrical halves, making it a perfect example of a shape with multiple lines of symmetry.
A) An isosceles trapezoid that is not a rhombus
An isosceles trapezoid has only one line of symmetry, which is the vertical line that passes through the midpoints of the two non-parallel sides. This does not meet the requirement for having exactly four lines of symmetry, making this option incorrect.
B) An equilateral triangle
An equilateral triangle has three lines of symmetry, each of which runs from a vertex to the midpoint of the opposite side. While it has multiple lines of symmetry, it does not have four, thus making this option incorrect.
C) A circle
A circle has an infinite number of lines of symmetry, as any line that passes through its center divides it into two equal halves. Although it has symmetry, it does not fit the criteria of having exactly four lines of symmetry, rendering this option incorrect.
D) A square
A square has exactly four lines of symmetry: two diagonals and two lines of symmetry that run horizontally and vertically through the center. This satisfies the condition of having exactly four lines of symmetry, confirming it as the correct answer.
Conclusion
In summary, a square is the only shape among the options that has exactly four lines of symmetry. The other options either fall short of this requirement or exceed it, affirming that only the square meets the criteria outlined in the question.