Types of Triangles: Classification & Properties Matrix
Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). This matrix lists each type with its side and angle properties and key theorem, plus a live classifier.
EquilateralAll 3 sides equalAll angles 60°
Isosceles2 equal sides2 base angles equal
ScaleneAll 3 sides unequalAll angles unequal
Acutea² + b² > c²All angles < 90°
Right-Angleda² + b² = c²Exactly one 90° angle
Obtusea² + b² < c²One angle > 90°
Triangle Type Classifier
Enter any three side lengths. The matching rows in the tables below are highlighted. Open this page with ?by=sides or ?by=angles to show only that classification.
| Triangle Name | Classification | Sides Property | Angles Property | Key Theorem | Copy |
|---|---|---|---|---|---|
| Equilateral | By Sides | All 3 equal | All 60° | 3 Lines of Symmetry | |
| Isosceles | By Sides | 2 equal sides | 2 base angles equal | Altitude bisects base | |
| Scalene | By Sides | All 3 unequal | All unequal | No symmetry lines | |
| Acute | By Angles | Any | All angles < 90° | a² + b² > c² | |
| Right-Angled | By Angles | Any | Exactly one 90° | a² + b² = c² (Pythagoras) | |
| Obtuse | By Angles | Any | One angle > 90° | a² + b² < c² |
| Combination | Possible? | Example Sides | Check: x² + y² vs c² | Angles | Copy |
|---|---|---|---|---|---|
| Equilateral + Acute | Yes | 6, 6, 6 | 36 + 36 = 72 > 36 | 60°, 60°, 60° | |
| Equilateral + Right | No | Not possible: all 3 angles are 60° | |||
| Equilateral + Obtuse | No | Not possible: all 3 angles are 60° | |||
| Isosceles + Acute | Yes | 5, 5, 6 | 25 + 25 = 50 > 36 | 53.13°, 53.13°, 73.74° | |
| Isosceles + Right | Yes | 1, 1, √2 | 1 + 1 = 2 = 2 | 45°, 45°, 90° | |
| Isosceles + Obtuse | Yes | 5, 5, 9 | 25 + 25 = 50 < 81 | 25.84°, 25.84°, 128.32° | |
| Scalene + Acute | Yes | 5, 6, 7 | 25 + 36 = 61 > 49 | 44.42°, 57.12°, 78.46° | |
| Scalene + Right | Yes | 3, 4, 5 | 9 + 16 = 25 = 25 | 36.87°, 53.13°, 90° | |
| Scalene + Obtuse | Yes | 2, 3, 4 | 4 + 9 = 13 < 16 | 28.96°, 46.57°, 104.48° | |
| Sides (a, b, c) | By Sides | By Angles | Check: x² + y² vs c² | Full Name | Copy |
|---|---|---|---|---|---|
| 3, 3, 3 | Equilateral | Acute | 9 + 9 = 18 > 9 | Equilateral (Acute) | |
| 7, 7, 7 | Equilateral | Acute | 49 + 49 = 98 > 49 | Equilateral (Acute) | |
| 5, 5, 6 | Isosceles | Acute | 25 + 25 = 50 > 36 | Acute Isosceles | |
| 5, 5, 8 | Isosceles | Obtuse | 25 + 25 = 50 < 64 | Obtuse Isosceles | |
| 6, 6, 10 | Isosceles | Obtuse | 36 + 36 = 72 < 100 | Obtuse Isosceles | |
| 4, 4, 7 | Isosceles | Obtuse | 16 + 16 = 32 < 49 | Obtuse Isosceles | |
| 10, 10, 14 | Isosceles | Acute | 100 + 100 = 200 > 196 | Acute Isosceles | |
| 3, 4, 5 | Scalene | Right | 9 + 16 = 25 = 25 | Right Scalene | |
| 6, 8, 10 | Scalene | Right | 36 + 64 = 100 = 100 | Right Scalene | |
| 5, 12, 13 | Scalene | Right | 25 + 144 = 169 = 169 | Right Scalene | |
| 8, 15, 17 | Scalene | Right | 64 + 225 = 289 = 289 | Right Scalene | |
| 10, 24, 26 | Scalene | Right | 100 + 576 = 676 = 676 | Right Scalene | |
| 5, 6, 7 | Scalene | Acute | 25 + 36 = 61 > 49 | Acute Scalene | |
| 6, 7, 8 | Scalene | Acute | 36 + 49 = 85 > 64 | Acute Scalene | |
| 4, 5, 6 | Scalene | Acute | 16 + 25 = 41 > 36 | Acute Scalene | |
| 7, 8, 9 | Scalene | Acute | 49 + 64 = 113 > 81 | Acute Scalene | |
| 2, 3, 4 | Scalene | Obtuse | 4 + 9 = 13 < 16 | Obtuse Scalene | |
| 4, 6, 9 | Scalene | Obtuse | 16 + 36 = 52 < 81 | Obtuse Scalene | |
| 7, 9, 12 | Scalene | Obtuse | 49 + 81 = 130 < 144 | Obtuse Scalene | |
| 9, 10, 12 | Scalene | Acute | 81 + 100 = 181 > 144 | Acute Scalene |
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Frequently Asked Questions
| Question | Answer |
|---|---|
| What are the types of triangles based on sides? | There are three: equilateral (all 3 sides equal), isosceles (2 equal sides) and scalene (all 3 sides different). |
| What are the types of triangles based on angles? | There are three: acute (all angles less than 90 degrees), right-angled (exactly one 90 degree angle) and obtuse (one angle greater than 90 degrees). |
| How can you tell if a triangle is acute, right or obtuse from its sides? | Let c be the longest side. If a² + b² > c² the triangle is acute, if a² + b² = c² it is right-angled, and if a² + b² < c² it is obtuse. For sides 5, 6, 7: 25 + 36 = 61 > 49, so it is acute. |
| Can a triangle be both right-angled and isosceles? | Yes. The 45-45-90 triangle has two equal legs and sides in the ratio 1 : 1 : sqrt(2). An equilateral triangle can never be right-angled or obtuse, because each of its angles is 60 degrees. |
| Is an equilateral triangle also an isosceles triangle? | Under the common definition of at least two equal sides, yes. This chart lists them separately because an equilateral triangle also has equal angles and 3 lines of symmetry. |
| Why can a triangle have only one right or obtuse angle? | The three angles add up to 180 degrees. Two angles of 90 degrees or more would already use all 180 degrees, leaving nothing for the third angle. |