Module 5 · Geometry and Measurement
Chapter 23: Triangles
Geometry & Trigonometry
5 topics
What this chapter covers
The 5 topics below make up Triangles on the Digital SAT. Click any topic to open its notes, examples and practice test.
1Classification of Triangles
2Triangle Congruence
3Similar Triangles
4Pythagorean Theorem
5Special Right Triangles
Study material & tests
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Formula Reference Sheet
This chapter
Core facts
| Angle sum | the three angles add to 180° |
|---|---|
| Pythagorean theorem | a² + b² = c² (right triangles) |
| Similarity | corresponding sides are in the same ratio |
Special right triangles
| 45-45-90 | legs equal; hypotenuse = leg × √2 |
|---|---|
| 30-60-90 | sides in ratio 1 : √3 : 2 |
| Common triples | 3-4-5, 5-12-13, 8-15-17 |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
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