In geometry, a line of symmetry is a line that can be drawn through a shape to create two halves that are mirror images of each other. If a shape can be folded in half along a line and the two halves match exactly, then the line is a line of symmetry.

Types of Lines of Symmetry

There are different types of lines of symmetry:

Horizontal Line of Symmetry: A line that divides a shape into two mirror image halves when the shape is folded along the line horizontally.
Vertical Line of Symmetry: A line that divides a shape into two mirror image halves when the shape is folded along the line vertically.
Diagonal Line of Symmetry: A line that divides a shape into two mirror image halves when the shape is folded along the line diagonally.

Finding Lines of Symmetry

To find the lines of symmetry for a shape, you can follow these steps:

Identify the shape you want to find the lines of symmetry for.
Visualize where you could fold the shape so that the two halves match exactly.
Draw the lines that represent the folds, and determine if they are lines of symmetry.

Examples

Let's look at some examples of shapes and their lines of symmetry:

Example 1: Triangle

A triangle has three sides. When a triangle is folded along a line that goes from the midpoint of one side to the opposite vertex, it will have one line of symmetry.

Example 2: Square

A square has four sides of equal length and four right angles. When a square is folded along a line that passes through the midpoints of opposite sides, it will have four lines of symmetry.

Study Guide

To study lines of symmetry, it's important to:

Understand the concept of symmetry and how lines of symmetry apply to different shapes.
Practice identifying lines of symmetry for various shapes, including triangles, squares, rectangles, circles, and other polygons.
Work on exercises that involve drawing lines of symmetry for given shapes.
Explore real-life examples of symmetry, such as in art, nature, and architecture.

By understanding and practicing lines of symmetry, you can develop a strong foundation in geometry and spatial reasoning.

◂Math Worksheets and Study Guides Sixth Grade. Algebraic Equations

The resources above cover the following skills:

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.