What are Similar Triangles?
**Similar triangles** are triangles that have the same shape but not necessarily the same size. If two triangles are similar, then:
- Their **corresponding angles** are congruent (equal).
- The lengths of their **corresponding sides** are proportional. This means the ratio of the lengths of the corresponding sides is constant, known as the **scale factor**.
For example, if $\triangle ABC$ is similar to $\triangle DEF$ ($$\triangle ABC \sim \triangle DEF$$), then:
- $\angle A \cong \angle D$, $\angle B \cong \angle E$, $\angle C \cong \angle F$
- $$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$$
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Video: Similar Triangles Explained!
Watch this video to visualize the properties of similar triangles! 🎥
Practice Problems
Use the properties of similar triangles to find the missing values!
Given $\triangle ABC \sim \triangle DEF$. If $AB=4, DE=8, AC=5$, what is $DF$?
If a triangle has angles of $50^\circ$ and $70^\circ$, what is the third angle?
Two triangles are similar. If a side in the first is 6 and the corresponding side in the second is 18, what is the scale factor?
A flagpole casts a 20ft shadow. A 6ft man casts a 4ft shadow. How tall is the flagpole?
⚡ Similar Triangles Speed Quiz
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