Similar

Property If two geometric objects or figures are similar, they have the same shape but are not necessarily the same size. Corresponding angles are congruent ($\cong$), and the ratio of corresponding sides is equal. For $\triangle ABC \sim \triangle DEF$, $\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$.

Examples Given $\triangle PQR \sim \triangle STU$, if $\angle P = 45^\circ$ and $\angle Q = 85^\circ$, then $\angle S = 45^\circ$ and $\angle T = 85^\circ$. If rectangle ABCD is similar to rectangle EFGH with $AB=4, BC=8$ and $EF=6, FG=12$, the side ratios are equal: $\frac{AB}{EF} = \frac{4}{6} = \frac{2}{3}$ and $\frac{BC}{FG} = \frac{8}{12} = \frac{2}{3}$.

Explanation Imagine a photo and its enlargement—that's what similar figures are all about! They have the exact same shape but can be different sizes. This means all their corresponding angles are perfectly equal, and the ratio of their corresponding sides is always the same. It’s like making a perfect copy, just zoomed in or out.