A kite has one line of symmetry. true or false?

Options

A. the diagonal AC
B. the diagonal BD
C. none of these
D. All of the above

Answer

To determine whether the statement "A kite has one line of symmetry" is true or false, we can analyze the properties of a kite.

### Step-by-Step Solution:

1. **Understanding the Kite Shape**: A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. For example, in kite ABCD, we have AB = AD and BC = DC.

2. **Identifying Lines of Symmetry**: A line of symmetry is a line that divides a shape into two identical halves. We need to find out how many such lines exist in a kite.

3. **Drawing the Kite**: Let's draw the kite ABCD. We can label the vertices as follows:
- A and B are the endpoints of one pair of equal sides.
- C and D are the endpoints of the other pair of equal sides.

4. **Testing for Symmetry**:
- We can draw a line from vertex A to vertex C. This line will divide the kite into two equal halves. The left side (A to B) is equal to the right side (A to D).
- Next, we can test the line from vertex B to vertex D. However, this line does not divide the kite into two equal halves because the lengths of the segments on either side of the line are not equal.

5. **Conclusion**: Since we found only one line (AC) that divides the kite into two equal halves, we conclude that a kite has only one line of symmetry.

6. **Final Answer**: Therefore, the statement "A kite has one line of symmetry" is **True**.