Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Line of Symmetry: An imaginary line that divides a figure into two identical halves. When a shape is folded along this line, both parts coincide or overlap exactly. Imagine a butterfly with its wings open; a line drawn down the middle of its body shows that both wings are mirror images of each other.
Vertical Symmetry: A line of symmetry that runs from the top to the bottom of a shape. For example, the capital letter '' or '' has a single vertical line of symmetry passing through the center.
Horizontal Symmetry: A line of symmetry that runs from the left to the right of a shape. For example, the capital letter '' or '' has a horizontal line of symmetry that divides the top half from the bottom half.
Symmetry in Regular Polygons: Shapes with all sides and angles equal are called regular polygons. A regular polygon has as many lines of symmetry as its number of sides. For instance, a square has lines of symmetry (horizontal, vertical, and diagonal lines), while an equilateral triangle has .
Reflection and Mirror Images: The line of symmetry acts like a mirror. In a reflection, the distance of every point on the original shape from the line of symmetry is equal to the distance of the corresponding point on the reflected image. This is often seen in nature, like a mountain reflecting in a still lake.
Patterns and Sequences: Patterns are arrangements of shapes, colors, or numbers that repeat according to a specific rule. For example, a sequence of shapes like 'Circle, Square, Circle, Square' is a repeating pattern.
Tessellations: A special type of pattern where shapes are repeated over and over to cover a surface without leaving any gaps or overlapping. Visualize a bathroom floor tiled with identical hexagonal or square tiles; this is a tessellation.
Growing Patterns: These are patterns that increase or decrease in size or quantity following a rule. For example, a pattern of dots where each step adds one more row of dots than the previous step ().
📐Formulae
(where is the number of sides)
(Infinite lines passing through the center)
💡Examples
Problem 1:
Determine the number of lines of symmetry for a regular hexagon and describe where they are located.
Solution:
Step 1: Identify the number of sides in a regular hexagon. A hexagon has sides. Step 2: Use the rule for regular polygons, which states that the number of lines of symmetry equals the number of sides. Step 3: Count the lines. There are lines passing through the opposite vertices (corners) and lines passing through the midpoints of opposite sides. Total lines of symmetry = .
Explanation:
Since a regular hexagon has equal sides and angles, any line passing through the center to opposite vertices or midpoints will divide it into two identical halves.
Problem 2:
Identify the rule and find the next two terms in the pattern:
Solution:
Step 1: Look at the relationship between the first and second terms: . Step 2: Check if this rule applies to the rest: and . The rule is 'multiply by '. Step 3: Calculate the next term: . Step 4: Calculate the term after that: . The next two terms are and .
Explanation:
This is a growing pattern where each subsequent number is double the previous number.