Module · Geometry
Chapter 20: Triangles
Geometry
6 topics
What this chapter covers
The 6 topics below make up Triangles on the GRE. Click any topic to open its notes, examples and practice test.
1Angle Sum & Exterior Angle
2Types of Triangles
3The Pythagorean Theorem
4Special Right Triangles (45-45-90, 30-60-90)
5Similar & Congruent Triangles
6Area of a Triangle
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Angles & sides
| Angle sum of a triangle | a + b + c = 180° |
|---|---|
| Exterior angle | = sum of the two remote interior angles |
| Triangle inequality | |a − b| < third side < a + b |
| Isosceles | equal sides ⇒ equal base angles |
Right triangles
| Pythagorean theorem | a² + b² = c² (c = hypotenuse) |
|---|---|
| Common triples | 3-4-5, 5-12-13, 8-15-17, 7-24-25 (and multiples) |
| 45-45-90 sides | 1 : 1 : √2 (leg : leg : hypotenuse) |
| 30-60-90 sides | 1 : √3 : 2 (opposite 30° : 60° : 90°) |
Area
| Any triangle | Area = ½ × base × height |
|---|---|
| Equilateral, side s | Area = (√3 / 4) × s² |
GRE reference
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