Classify congruence transformations

Learning Objectives Define a congruence transformation (isometry) and its properties. Identify the four types of congruence transformations: translation, reflection, rotation, and glide reflection. Classify a transformation as a direct or opposite isometry by analyzing the orientation of the figure. Use coordinate rules to describe a specific congruence transformation. Classify a transformation by analyzing the coordinates of a pre-image and its image. Prove two figures are congruent by describing a sequence of congruence transformations that maps one onto the other. Ever wonder how a video game character moves across the screen or how a pattern is created on wallpaper without changing size or shape? 🎮 That's the power of congruence transformations! In this tutorial,...

TermDefinitionExample Congruence Transformation (Isometry)A transformation that preserves distance and angle measure. The pre-image (original figure) and the image (transformed figure) are congruent.Sliding a triangle 5 units to the right. The new triangle is identical in size and shape to the original. TranslationA transformation that slides every point of a figure the same distance in the same direction along a vector.If point P(2, 3) is translated by the vector <4, -1>, its image is P'(6, 2). ReflectionA transformation that flips a figure across a line, called the line of reflection, creating a mirror image.Reflecting the point P(2, 3) across the x-axis results in the image P'(2, -3). RotationA transformation that turns a figure about a fixed point, called the center of...

Translation Rule T_{a,b}(x, y) = (x + a, y + b) This rule describes a translation. Every point (x, y) is moved 'a' units horizontally and 'b' units vertically. The vector <a, b> is the translation vector. Reflection Rules Reflection across x-axis: (x, y) -> (x, -y) Reflection across y-axis: (x, y) -> (-x, y) Reflection across line y = x: (x, y) -> (y, x) These rules describe reflections across common lines in the coordinate plane. The sign of one or both coordinates changes, or the coordinates are swapped. Rotation Rules (about the origin) 90° counter-clockwise: (x, y) -> (-y, x) 180°: (x, y) -> (-x, -y) 270° counter-clockwise: (x, y) -> (y, -x) These rules describe counter-clockwise rotations about the origin (0,0). For cl...