Math 8B unit two lesson eight transformation and congruences
In this lesson, you will learn about transformations and congruences in mathematics.
A transformation is a change in the position, shape, or size of a figure or shape. There are four main types of transformations: translations, rotations, reflections, and dilations.
1. Translations: A translation is a "slide" of a figure from one position to another, without changing its shape or size. To perform a translation, you move every point of the figure the same distance in the same direction.
2. Rotations: A rotation is a "turn" of a figure around a point, called the center of rotation. To perform a rotation, you measure the angle of rotation and direction (clockwise or counterclockwise) and move each point of the figure that angle around the center of rotation.
3. Reflections: A reflection is a "flip" of a figure across a line, called the line of reflection. To perform a reflection, you draw a line of reflection and then find the perpendicular distance between each point and the line. Finally, you move each point across the line that same distance in the opposite direction.
4. Dilations: A dilation is a "stretch" or "shrink" of a figure, either larger or smaller, known as an enlargement or a reduction. To perform a dilation, you choose a center of dilation and a scale factor. Then, you multiply the coordinates of each point by the scale factor to determine the new position.
Congruent figures are figures that have the same shape and size. In other words, if you can move one figure onto another using one or more of the four transformations without changing its shape or size, the figures are congruent. Congruent figures have corresponding angles and sides that are equal.
In this lesson, you will practice identifying and performing transformations and determining if figures are congruent. You will also learn about congruence shortcuts, such as the Side-Angle-Side (SAS) congruence criterion and the Angle-Side-Angle (ASA) congruence criterion.
By understanding transformations and congruences, you will be able to analyze and describe geometric shapes and figures accurately. You will also be able to determine if objects are identical or congruent in real-life situations, such as architecture, design, and nature.