Symmetry

Learning Objectives Identify lines of symmetry in two-dimensional shapes. Describe and perform a reflection of a shape across a line. Describe and perform a translation (slide) of a shape on a coordinate plane. Describe and perform a rotation (turn) of a shape around a given point. Distinguish between reflection, translation, and rotation. Understand that transformations preserve the size and shape of figures. Identify real-world examples of symmetry and transformations. Have you ever looked in a mirror and seen your exact copy? Or watched a car move straight down the road? 🚗 These are everyday examples of mathematical ideas called symmetry and transformations! In this lesson, we'll explore how shapes can be perfectly balanced (symmetry) and how they can move around...

TermDefinitionExample SymmetrySymmetry means that a shape or object looks the same after being flipped, slid, or turned in a certain way.A butterfly has line symmetry because its left wing is a mirror image of its right wing. Line of SymmetryA line of symmetry is an imaginary line that divides a shape into two identical halves that are mirror images of each other.A square has four lines of symmetry: two horizontal/vertical and two diagonal. TransformationA transformation is a way to move a geometric figure from one position to another without changing its size or shape.Sliding a book across a table is a type of transformation called a translation. Reflection (Flip)A reflection is a transformation that flips a figure over a line, called the line of reflection, creating a mirror image.Your...

Rule of Reflection `P \rightarrow P'` where P' is the mirror image of P across the line of reflection L. The distance from any point P to L is equal to the distance from its image P' to L, and the line segment PP' is perpendicular to L. When reflecting a shape, each point on the shape moves to an equal distance on the opposite side of the line of reflection. The shape 'flips' over the line. Rule of Translation `P(x, y) \rightarrow P'(x+a, y+b)` where P is translated 'a' units horizontally and 'b' units vertically. To translate a shape, you add or subtract the same amount from the x-coordinate (for horizontal movement) and the y-coordinate (for vertical movement) of every point in the shape. The shape 'slides' w...