Symmetry and congruence are important ideas when it comes to understanding shapes in geometry. They help us define and compare different shapes.

Symmetry

1. What is Symmetry?
   A shape is symmetrical if you can split it down the middle and get two equal parts.

2. Types of Symmetry:

   • Reflection Symmetry: You can fold the shape along a line, and both sides will look the same (like isosceles triangles).
   • Rotational Symmetry: If you spin the shape around a center point, it looks the same at certain angles (for example, a regular hexagon can be turned and still match itself 6 times).

Congruence

1. What is Congruence?
   Two shapes are congruent if they are exactly the same in both shape and size.

2. How Do We Know if Shapes are Congruent?

   • For triangles, we have some rules: one is called Side-Side-Side (SSS), another is Angle-Side-Angle (ASA), and the last is Side-Angle-Side (SAS).
   • For four-sided shapes (quadrilaterals), we look at their sides and angles to see if they are congruent.

How This Affects Classification

• Triangles: We can group triangles by their angles (acute, right, obtuse) and their sides (scalene, isosceles, equilateral).
• Quadrilaterals: These can be sorted into types like parallelograms and trapezoids, based on whether their sides and angles match.

When we think about symmetry and congruence, it becomes easier for students to see how different shapes are connected to one another.