Classification of Triangles

Classification of Triangles by Sides

• Triangles can be classified based on the lengths of their sides.
• Equilateral Triangles: All three sides are equal; represented by marking each side with the same symbol.
• Isosceles Triangles: Two sides are equal; any combination of two sides can be equal while the third side is different.
• Scalene Triangles: No sides are equal; each side has a different length.

Classification of Triangles by Angles

• Triangles can also be classified based on the measures of their angles.
• Acute Triangles: All angles are less than 90 degrees.
• Right Triangles: One angle is exactly 90 degrees; also called right-angled triangles.
• Obtuse Triangles: One angle is greater than 90 degrees, making it obtuse.

Important Angle Facts

• An angle less than 90 degrees is termed acute.
• An angle exactly 90 degrees is a right angle.
• An angle greater than 90 degrees is an obtuse angle.

Additional Notes

• In a right triangle, only one angle can be right; having two right angles is not possible within a triangle's geometric constraints.

Classification of Triangles by Sides

• Triangles can be categorized based on side lengths.
• Equilateral Triangles: All sides are identical in length, denoted by the same symbol on each side.
• Isosceles Triangles: Two sides have equal lengths; the third side differs, allowing for various combinations of equal sides.
• Scalene Triangles: All sides are distinct in length, with no equality among them.

Classification of Triangles by Angles

• Angles also serve as a basis for triangle classification.
• Acute Triangles: Each of the three angles measures less than 90 degrees, resulting in all acute angles.
• Right Triangles: One angle measures exactly 90 degrees; commonly referred to as right-angled triangles.
• Obtuse Triangles: One angle exceeds 90 degrees, categorizing it as obtuse and impacting the overall shape.

Important Angle Facts

• An angle measuring less than 90 degrees is identified as acute.
• An angle measuring precisely 90 degrees is defined as a right angle.
• An angle that measures more than 90 degrees is considered obtuse.

Additional Notes

• In any right triangle, only one angle can be a right angle; having two right angles contradicts geometric principles.

Classification of Triangles by Sides

• Triangles can be categorized based on side lengths.
• Equilateral Triangles: All sides are identical in length, denoted by the same symbol on each side.
• Isosceles Triangles: Two sides have equal lengths; the third side differs, allowing for various combinations of equal sides.
• Scalene Triangles: All sides are distinct in length, with no equality among them.

Classification of Triangles by Angles

• Angles also serve as a basis for triangle classification.
• Acute Triangles: Each of the three angles measures less than 90 degrees, resulting in all acute angles.
• Right Triangles: One angle measures exactly 90 degrees; commonly referred to as right-angled triangles.
• Obtuse Triangles: One angle exceeds 90 degrees, categorizing it as obtuse and impacting the overall shape.

Important Angle Facts

• An angle measuring less than 90 degrees is identified as acute.
• An angle measuring precisely 90 degrees is defined as a right angle.
• An angle that measures more than 90 degrees is considered obtuse.

Additional Notes

• In any right triangle, only one angle can be a right angle; having two right angles contradicts geometric principles.