1. **Problem statement:** (a) Shade one more small triangle in the large equilateral triangle subdivided into smaller triangles so that the figure has one line of symmetry. (b) Shade two more small squares in the 4x4 grid so that the figure has rotational symmetry of order 2. 2. **Understanding symmetry:** - A line of symmetry means the figure is mirrored exactly across a line. - Rotational symmetry of order 2 means the figure looks the same after a rotation of 180 degrees. 3. **Part (a) solution:** - The large triangle is equilateral, so the line of symmetry is likely vertical through the center. - Two small triangles are shaded near the left and right parts. - To create one line of symmetry, shade the small triangle that is exactly opposite the unpaired shaded triangle across the vertical center line. - This means shading the small triangle that mirrors the existing shaded triangle on the left or right side. 4. **Part (b) solution:** - The 4x4 grid has two shaded squares near upper-left and center-right. - Rotational symmetry of order 2 means after rotating 180 degrees, the shaded squares map onto shaded squares. - To achieve this, shade the two squares that are the 180-degree rotations of the existing shaded squares. - For example, if one shaded square is at position (row 1, column 2), shade the square at (row 4, column 3) because rotating 180 degrees maps (1,2) to (4,3) in a 4x4 grid. **Final answers:** - (a) Shade the small triangle symmetric to the existing shaded triangle across the vertical center line. - (b) Shade the two squares that are 180-degree rotational images of the existing shaded squares. This completes the symmetry requirements.