Yes, a shape can have more than one line of symmetry. An excellent example of this is a regular hexagon, which has six lines of symmetry. Each line of symmetry passes through two opposite vertices, dividing the hexagon into two congruent parts that are mirror images of each other. The concept of multiple lines of symmetry is not restricted to hexagons; numerous shapes, especially regular polygons, exhibit this property. For instance, a square has four lines of symmetry, an equilateral triangle has three, and a circle has infinite lines of symmetry. Understanding multiple lines of symmetry aids in comprehending the inherent balance and proportionality in various shapes.

Symmetry is a fundamental concept that extends beyond geometry, permeating various areas of mathematics and science. In mathematics, symmetry is explored in algebra through symmetric functions and in calculus through even and odd functions. In physics, symmetry principles underpin numerous laws and theories, such as the conservation laws in classical and quantum mechanics. In chemistry, molecular symmetry explains various physical and chemical properties of compounds. Furthermore, in biology, symmetry is observed in the body structures of various organisms, aiding in understanding evolutionary biology and developmental biology. Thus, symmetry serves as a unifying concept, providing insights and explanations across diverse scientific disciplines.

Understanding the properties of shapes significantly enhances problem-solving skills in mathematics by providing a foundational knowledge that can be applied in various mathematical challenges and real-world problems. Knowing the properties of shapes, such as angles, sides, and symmetry, allows students and professionals to identify, classify, and analyse shapes and patterns, which is crucial in geometry, trigonometry, and even calculus. It enables them to make predictions, formulate hypotheses, and derive conclusions about a shape or a system. Moreover, it aids in developing logical reasoning and analytical thinking, as individuals learn to deduce unknown properties or measurements by applying known properties and theorems, thereby fostering a systematic and logical approach towards problem-solving in mathematics and beyond.

Grasping the properties of sides in polygons is pivotal in geometry as it aids in identifying and classifying different shapes and determining their characteristics. For example, knowing that all sides of an equilateral triangle are equal allows mathematicians and scientists to make specific predictions and calculations about its other properties, such as its angles and symmetry. In practical terms, understanding the properties of sides is vital in various fields like architecture, design, and engineering, where precise calculations and predictions are imperative to create stable, symmetrical, and aesthetically pleasing structures. Moreover, it enables problem-solving in advanced geometrical concepts and theorems.

Understanding the properties of angles can significantly impact various real-world scenarios, particularly in construction and design. For instance, when architects design buildings, they utilise angles to create structures that are both aesthetically pleasing and structurally sound. Acute and obtuse angles might be used to create interesting visual effects, while right angles are often employed to ensure stability. Engineers also apply angle properties in constructing roads, bridges, and ramps, ensuring that they are safe and functional. In sports, athletes and coaches analyse angles to enhance performance, such as calculating the best angle to kick a football to score a goal or to throw a basketball to make a basket. Thus, the properties of angles permeate numerous practical applications, underpinning various professions and activities.