Question

which of the following shapes have one line of symmetry but no rotational symmetry? select all that apply.

Explanation:

Step1: Analyze each shape's symmetry

- **First shape (top):** Likely has rotational symmetry (e.g., 90 - degree rotation) and multiple lines of symmetry.
- **Second shape (pentagon - like):** A regular - looking pentagon - shaped figure, likely has 5 lines of symmetry and rotational symmetry (72 - degree rotation).
- **Third shape (T - like):** Check line symmetry: It has one vertical line of symmetry. Check rotational symmetry: Rotating 180 degrees or other angles won't map it onto itself, so no rotational symmetry.
- **Fourth shape (cross - like):** Likely has multiple lines of symmetry (vertical and horizontal) and rotational symmetry (180 - degree rotation).
- **Fifth shape (trapezoid - like):** If it's an isosceles trapezoid, it has one line of symmetry, but also rotational symmetry? No, an isosceles trapezoid has no rotational symmetry (except 360 - degree, which is trivial). Wait, but let's re - check the third shape. The third shape (the T - shaped one) has one line of symmetry (vertical) and no rotational symmetry. The isosceles trapezoid - like shape also has one line of symmetry and no rotational symmetry, but the T - shaped one is more distinct. Wait, maybe the third shape (the one with a small rectangle attached to a larger rectangle on the left, making a T - like shape) is the one. Wait, also the last shape (the rounded rectangle - like) has one line of symmetry (vertical) and no rotational symmetry? Wait, no, the T - shaped one: when we rotate it 180 degrees, the small rectangle would be on the right, which is not the same as the original. So it has one line of symmetry (vertical) and no rotational symmetry. The isosceles trapezoid - like shape: if it's a non - isosceles trapezoid, it has no line of symmetry. If it's isosceles, one line. But the T - shaped one is a better candidate. Wait, let's re - evaluate:
The third shape (the one with a small rectangle on the left of a larger square - like rectangle) has a vertical line of symmetry. When we rotate it by 180 degrees, the small rectangle would be on the right, so it doesn't match the original. So no rotational symmetry. And only one line of symmetry. The fifth shape (the trapezoid) - if it's isosceles, one line of symmetry, and no rotational symmetry (since rotating it 180 degrees would flip the top and bottom, but in an isosceles trapezoid, the legs are equal, but the top and bottom bases are different lengths, so rotating 180 degrees won't map it onto itself). Wait, but the T - shaped one is more clearly having one line of symmetry and no rotational symmetry. Also, the last shape (the rounded top rectangle) has one vertical line of symmetry and no rotational symmetry. But among the options, the third shape (the T - like) and the fifth (trapezoid) and the last (rounded) need to be checked again. Wait, the third shape: let's visualize. The left - most shape (third in the list) is a combination of a small rectangle attached to the left side of a larger rectangle, forming a sort of T - shape (but with the stem on the left). A vertical line through the center will map the left and right (but the left has the small rectangle, right has the large rectangle's left part? Wait, no, maybe horizontal? Wait, no, the small rectangle is on the left, so a vertical line of symmetry: the left part (small rectangle) and the right part (the larger rectangle's left - most part) would be symmetric. Wait, maybe I got the line wrong. Wait, maybe the third shape has a vertical line of symmetry. When we rotate it 180 degrees, the small rectangle would be on the right, which is not the same as the original, so no rotational symmetry. The last shape (the one with a rounded top and straight bottom) has a vertical line of symmetry and no rotational symmetry. But the T - shaped one is more likely the answer. Wait, maybe the third shape (the one with the small rectangle on the left, making a T - like shape) is the correct one. Or the fifth (trapezoid) or the last (rounded). Wait, the question is to select all that apply. But let's check each:

1. First shape: Rotational symmetry (yes), multiple lines (yes) → no.
2. Second shape: Multiple lines, rotational → no.
3. Third shape: One line (vertical), no rotational → yes.
4. Fourth shape: Multiple lines, rotational → no.
5. Fifth shape (trapezoid - like): If isosceles, one line, no rotational → yes.
6. Last shape (rounded rectangle - like): One line (vertical), no rotational → yes.

But maybe the third shape (the T - shaped one) and the fifth (trapezoid) and the last (rounded) are the ones. Wait, but the T - shaped one: let's confirm. The T - shaped figure (third from top) has a vertical line of symmetry. Rotating it 180 degrees would invert it, so the small rectangle would be on the right, which is not the same as the original, so no rotational symmetry. The isosceles trapezoid - like figure (fifth) has one line of symmetry (vertical) and no rotational symmetry (since rotating 180 degrees would swap the top and bottom, but the top and bottom are different in length? No, in an isosceles trapezoid, the top and bottom bases are parallel and the legs are equal. Rotating 180 degrees would map the top base to the bottom base and vice - versa, but since they are parallel and the legs are equal, does it map onto itself? No, because the orientation of the legs would be reversed. So an isosceles trapezoid has no rotational symmetry (except 360 degrees). The last shape (rounded top, straight bottom) has one vertical line of symmetry and no rotational symmetry (rotating 180 degrees would put the rounded part at the bottom, which is not the same as the original).

But maybe the intended answer is the third shape (the T - shaped one) or the fifth (trapezoid) or the last (rounded). Wait, looking at the options, the third shape (the one with the small rectangle on the left, making a T - like shape) is a common example of a shape with one line of symmetry and no rotational symmetry. Also, the last shape (the rounded rectangle - like) has one line of symmetry and no rotational symmetry. But maybe the third shape is the answer.

Step2: Confirm the selection

After analyzing each shape's line and rotational symmetry, the shape with one line of symmetry and no rotational symmetry is the third shape (the T - shaped one, or the one with a small rectangle attached to the left of a larger rectangle) and also the fifth (trapezoid - like) and the last (rounded - top) maybe. But likely the third shape (the T - shaped one) is the main candidate. Wait, maybe the third shape (the one with the small rectangle on the left, forming a T - like figure) is the correct one.

Answer:

The third shape (the one with a small rectangle attached to the left of a larger rectangle, making a T - like shape) (or the fifth shape - trapezoid - like, or the last shape - rounded - top, depending on the exact figures, but likely the third or fifth or last. But based on typical problems, the T - shaped one or the isosceles trapezoid - like or the rounded - top. However, in the given options, the third shape (the T - shaped one) is a common example. So the answer is the third shape (the one with the small rectangle on the left of a larger rectangle, i.e., the third option in the list of shapes).