Which of the following capital letters of the English alphabet has more than one line of symmetry?

Introduction / Context:
This question tests knowledge of symmetry, specifically lines of symmetry in capital letters of the English alphabet. A line of symmetry divides a shape into two mirror image halves. Some letters have no line of symmetry, some have exactly one, and a few have more than one line of symmetry. The problem asks which letter among the given options has more than one line of symmetry.

Given Data / Assumptions:

• We are dealing with capital letters A, C and O.
• We consider the standard block style of these letters as used in basic geometry discussions.
• A line of symmetry is a straight line such that reflecting the letter across that line leaves the letter unchanged.
• The question focuses on letters with more than one line of symmetry, not just at least one.
• We assume an idealized geometric representation of the letters.

Concept / Approach:
To solve this, we must visualize each letter and identify possible reflection lines. A has one vertical line of symmetry in most standard fonts. C, drawn as an open curve, usually does not have a vertical line of symmetry and does not have more than one clear line of symmetry. The letter O, when drawn as a perfect circle or an ideal ellipse, has multiple lines of symmetry: in the circular case, infinitely many, and even in an ideal symmetric oval, at least two distinct lines, one vertical and one horizontal. Therefore O clearly has more than one line of symmetry.

Step-by-Step Solution:
Step 1: Consider the letter A. It is typically drawn as two slanting sides joined by a horizontal bar. It has a vertical line of symmetry down the middle, but no horizontal line of symmetry because the top and bottom are different shapes.Step 2: Since A has exactly one line of symmetry, it does not meet the condition of having more than one line of symmetry.Step 3: Now consider the letter C. It looks like a curved arc open on one side. In a standard block style, it has no vertical line of symmetry because the open side is on one side only. It also has no horizontal symmetry, since the top and bottom curves are not mirror images about a horizontal axis.Step 4: Because C has no clear line of symmetry in the idealized sense, it certainly does not have more than one line of symmetry.Step 5: Finally, consider the letter O. If we model O as a perfect circle, it has infinitely many lines of symmetry through its center. Even if we model it as a symmetric ellipse, it still has at least two symmetry lines, one vertical and one horizontal.Step 6: Thus, among A, C and O, only O has more than one line of symmetry.

Verification / Alternative check:
An easy check is to imagine folding a printed letter on paper. For A, folding along a vertical line through the middle aligns the two halves, but any other fold will not. For C, no straight fold will give perfect overlap. For O, one can fold vertically, horizontally and along many diagonal lines through the center, and the two halves will match exactly. This simple folding test confirms that O has more than one line of symmetry.

Why Other Options Are Wrong:
Option a, A, has only one vertical line of symmetry, so it does not satisfy the requirement of more than one. Option b, C, has at most one approximate line of symmetry in certain stylized fonts and often none in an ideal geometric interpretation, but definitely not more than one. Option d, All of the above, is incorrect because A and C do not both have more than one line of symmetry. Only O clearly meets the stated condition.

Common Pitfalls:
Students may misread the phrase and focus on letters that have at least one line of symmetry instead of more than one. Another source of confusion is relying on a particular stylized font rather than the standard geometric form. It is important to apply the formal idea of reflection symmetry rather than rough visual guesses.

Final Answer:
The capital letter that has more than one line of symmetry among the given options is O.