Side lengths and angle measures of similar figures

Learning Objectives Define and identify similar figures. Identify corresponding sides and angles in similar figures. Determine unknown side lengths of similar figures using scale factor and proportions. Determine unknown angle measures of similar figures. Explain the relationship between corresponding angles and sides in similar figures. Apply properties of similar figures to solve real-world problems. Have you ever seen a small model car that looks exactly like a real car, just shrunken down? 🚗 What makes them look so alike, even though they're different sizes? In this lesson, you'll discover the fascinating properties of similar figures, where shapes have the same form but different sizes. We'll explore how their side lengths are related by a constant scal...

TermDefinitionExample Similar FiguresTwo figures are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal, and their corresponding side lengths are proportional.A photograph and its enlargement are similar figures. A small triangle and a larger triangle with the same angle measures are similar. Corresponding SidesSides that are in the same relative position in two or more similar figures. They are proportional to each other.In two similar triangles ABC and DEF, side AB corresponds to side DE, side BC corresponds to side EF, and side CA corresponds to side FD. Corresponding AnglesAngles that are in the same relative position in two or more similar figures. They have equal measures.In two similar triangles ABC and DEF, angle...

Corresponding Angles Rule for Similar Figures If two figures are similar, then their corresponding angles are congruent (have equal measures). This rule means that if you know the measure of an angle in one figure, you automatically know the measure of its corresponding angle in any similar figure. For example, if $\triangle ABC \sim \triangle DEF$, then $\angle A \cong \angle D$, $\angle B \cong \angle E$, and $\angle C \cong \angle F$. Proportional Sides Rule for Similar Figures If two figures are similar, then the ratio of the lengths of their corresponding sides is constant. This constant ratio is called the scale factor. For example, if $\triangle ABC \sim \triangle DEF$, then $\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = k$, where $k$ is the scale factor. Scale...