1. **Problem Statement:** We need to find: - The number of lines of symmetry for shapes S and T. - The order of rotational symmetry for shapes S and T. - Whether the number of lines of symmetry always equals the order of rotational symmetry. 2. **Lines of Symmetry:** - A line of symmetry divides a shape into two mirror-image halves. - For shape S (a five-pointed star or pentagram), it has 5 lines of symmetry because each line passes through a point and the opposite indentation. - For shape T (a square with four triangular extensions), it has 4 lines of symmetry: 2 along the diagonals and 2 along the midlines of the square. 3. **Order of Rotational Symmetry:** - The order of rotational symmetry is the number of times a shape maps onto itself during a full 360° rotation. - Shape S has rotational symmetry of order 5 because it looks the same every 72° ($\frac{360}{5}=72$). - Shape T has rotational symmetry of order 4 because it looks the same every 90° ($\frac{360}{4}=90$). 4. **Comparison:** - For shape S, lines of symmetry = 5 and order of rotational symmetry = 5. - For shape T, lines of symmetry = 4 and order of rotational symmetry = 4. 5. **General Rule:** - It is often true for regular polygons and symmetric shapes that the number of lines of symmetry equals the order of rotational symmetry. - However, this is not always true for all shapes. **Final answers:** - Shape S: 5 lines of symmetry, order of rotational symmetry 5. - Shape T: 4 lines of symmetry, order of rotational symmetry 4. - The statement that the number of lines of symmetry always equals the order of rotational symmetry is not always true, but it holds for these shapes.