Similar Triangles β Complete SAT Guide
π― Why This Matters on the SAT
Similar triangles concepts appear in 2β4 questions on a typical SAT Math section, often embedded in geometry, coordinate geometry, and word problems. Mastering this topic gives you a reliable edge across multiple question types. This lesson covers every configuration, formula, and strategy you need.
1. What Are Similar Triangles?
Similar triangles are triangles that have the same shape but not necessarily the same size.
| Property | Similar (βΌ) | Congruent (β ) |
|---|---|---|
| Same shape | β Yes | β Yes |
| Same size | β Not necessarily | β Yes |
| Equal angles | β Yes | β Yes |
| Equal sides | β Proportional | β Yes |
Symbol: $\triangle ABC \sim \triangle DEF$ means triangle ABC is similar to triangle DEF.
Correspondence matters! The order of vertices tells you which parts match: $A \leftrightarrow D$, $B \leftrightarrow E$, $C \leftrightarrow F$.
Correspondence matters! The order of vertices tells you which parts match: $A \leftrightarrow D$, $B \leftrightarrow E$, $C \leftrightarrow F$.
Interactive visualization β available in the full lesson
2. Properties of Similar Triangles
π Equal Corresponding Angles
If $\triangle ABC \sim \triangle DEF$, then:
$$\angle A = \angle D, \quad \angle B = \angle E, \quad \angle C = \angle F$$π Proportional Corresponding Sides
The ratios of all corresponding sides are equal:
$$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = k$$π The Scale Factor ($k$)
The scale factor is the common ratio of corresponding sides.
$k > 1$
Second triangle is larger
Second triangle is larger
$k = 1$
Triangles are congruent
Triangles are congruent
$k < 1$
Second triangle is smaller
Second triangle is smaller
Identifying Corresponding Sides: Sides opposite equal angles correspond to each other. The longest side of one triangle corresponds to the longest side of the other, and so on.