Symmetry worksheet for Grade 5 students, focusing on completing symmetrical shapes on grid paper.

This is a Grade 5 Maths worksheet on "Symmetry". The task is to "Draw the other half of each symmetrical shape." Each shape is drawn on a dot grid with a vertical line of symmetry, and you need to complete the shape by reflecting the given half across this line.

I will solve this problem by describing how to complete each shape (a through i) based on the principles of reflectional symmetry. For each shape, I will identify the key points on the given half and describe where their mirror images should be placed on the other side of the vertical line.

Let's begin by examining each shape one by one.

Shape a

- This is a right triangle.
- The vertical line of symmetry is along the right edge of the triangle.
- To complete it, I need to reflect the hypotenuse and the base across the line.
- The top vertex is on the line of symmetry, so it stays in place.
- The bottom-left vertex needs to be mirrored to the bottom-right.
- Connecting these points will form a larger isosceles triangle.

Shape b

- This is a complex polygon with several vertices.
- I need to find the mirror image of each vertex across the vertical line.
- The top vertex is on the line, so it remains.
- The "notch" on the left side must be mirrored to the right side.
- The bottom vertex on the left must be mirrored to the bottom right.
- Connecting these mirrored points will create a symmetrical shape resembling an arrow or a stylized letter 'Y'.

Shape c

- This shape looks like half of an hourglass or two triangles joined at the apex.
- The top and bottom vertices are on the line of symmetry.
- The middle "V" shape on the left must be mirrored to the right.
- Completing this will form a symmetrical hourglass or bowtie shape.

Shape d

- This is a complex, jagged shape.
- I need to mirror each point across the vertical line.
- The top point is on the line.
- The "M" shape on the left must be mirrored to form a complete "W" or "M" depending on the perspective.
- The zigzag at the bottom must also be mirrored.
- The completed shape will be a symmetrical, abstract figure.

Shape e

- This is a rectangle with indentations.
- The top and bottom edges are horizontal and on the line of symmetry.
- The indentations on the left must be mirrored on the right.
- The completed shape will be a symmetrical rectangle with notches on both sides.

Shape f

- This resembles half of a letter 'E'.
- The horizontal lines must be extended symmetrically to the right.
- The vertical line on the left must be mirrored to the right.
- The completed shape will be a full letter 'E'.

Shape g

- This has a semicircle on the left attached to a rectangle.
- The semicircle must be mirrored to form a full circle.
- The rectangle must be extended symmetrically to the right.
- The completed shape will be a circle attached to a rectangle on both sides.

Shape h

- This is similar to shape c but with a different orientation.
- It looks like half of a butterfly or an hourglass.
- The top and bottom vertices are on the line of symmetry.
- The "V" shapes on the left must be mirrored to the right.
- The completed shape will be a symmetrical butterfly or hourglass.

Shape i

- This is a right triangle with the vertical line of symmetry along its right edge.
- The top vertex is on the line.
- The bottom-left vertex must be mirrored to the bottom-right.
- Connecting these points will form a larger isosceles triangle, similar to shape a.

In summary, to solve this worksheet, you need to reflect each given half-shape across the vertical line of symmetry by finding the mirror image of each vertex and connecting them in the same order. This will complete each shape into a symmetrical figure.

The solution involves understanding that for any point on the given half, its mirror image is the same distance from the line of symmetry but on the opposite side. By applying this principle to all vertices, you can accurately draw the missing half of each shape.