Introduction to similar solids

Learning Objectives Define 'similar shapes' as shapes that have the same shape but different sizes. Identify corresponding vertices and sides in similar 2D shapes plotted on a coordinate plane. Apply a given scale factor to the coordinates of a 2D shape to create a similar shape. Plot original and scaled shapes on the coordinate plane. Understand that scaling a shape on the coordinate plane changes its size but not its angles. Explain how the concept of similar 2D shapes relates to understanding similar 3D solids. Have you ever seen a small toy car and a real car that look exactly alike, just different sizes? 🚗 That's the idea behind similar shapes! In this lesson, we'll explore what makes shapes 'similar' using the coordinate plane. We'l...

TermDefinitionExample Coordinate PlaneA flat surface made of a grid, used to locate points using ordered pairs of numbers (x, y).Plotting the point (3, 2) means moving 3 units right and 2 units up from the origin. OriginThe starting point (0,0) on the coordinate plane where the x-axis and y-axis meet.If you start at the origin and move 5 units right, you are at (5,0). Similar ShapesShapes that have the exact same shape but can be different sizes. One is a scaled version of the other.A small square and a large square are similar shapes because they both have four equal sides and four right angles. Scale FactorThe number by which all the side lengths of a shape are multiplied to create a similar shape. It tells you how much bigger or smaller the new shape is.If a square with sides of 2 unit...

Rule for Scaling Coordinates from the Origin $(x, y) \rightarrow (k \cdot x, k \cdot y)$ To scale a shape on the coordinate plane by a scale factor 'k' from the origin, multiply both the x-coordinate and the y-coordinate of each vertex by 'k'. This creates a new shape that is similar to the original. Rule for Identifying Similar Shapes $\text{Corresponding angles are equal}$ and $\frac{\text{Side 1 of Shape A}}{\text{Side 1 of Shape B}} = \frac{\text{Side 2 of Shape A}}{\text{Side 2 of Shape B}} = k$ Two shapes are similar if all their corresponding angles are the same, AND all their corresponding side lengths are proportional (meaning they are multiplied by the same scale factor 'k').