Module 4 · Geometry
Chapter 43: Triangles
Geometry
4 topics
What this chapter covers
The 4 topics below make up Triangles on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
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Formula Reference Sheet
This chapter
Sides, area & similarity
| Angle sum / exterior angle | A + B + C = 180°; exterior = sum of two remote interior angles |
|---|---|
| Triangle inequality | |b − c| < a < b + c |
| Basic area | Area = ½ × base × height |
| Heron’s formula | Area = √[s(s−a)(s−b)(s−c)], s = (a+b+c)/2 |
| Similar triangles (AA) | Area ratio = (corresponding side ratio)² |
| Basic Proportionality (Thales) | DE ∥ BC ⇒ AD/DB = AE/EC |
Right triangles & centres
| Pythagoras | hypotenuse² = leg₁² + leg₂² (a² + b² = c²) |
|---|---|
| Common triples | 3-4-5, 5-12-13, 8-15-17, 7-24-25 (and multiples) |
| Centroid divides median | 2 : 1 from the vertex |
| Circumradius | R = abc / (4 × Area) |
| Inradius | r = Area / s, so Area = r × s |
| Equilateral (side a) | Area = (√3/4)a²; R = a/√3; r = a/(2√3) |
CAT reference
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