Important Formulas: Triangles

Different Criterion for Congruence of the triangles

Some Important Points on Triangles

• Equilateral triangle: All three sides equal. Each angle equals 60°.
• Isosceles triangle: Two sides equal; base angles equal.
• Scalene triangle: All sides (and all angles) are unequal.
• Right triangle: One angle is 90°.
• Acute triangle: All three angles are less than 90°.
• Obtuse triangle: One angle is greater than 90° and the other two are acute.
• Median: A line Segment joining the corner of the triangle to the midpoint of the opposite side of the triangle
• Altitude: A line Segment from the corner of the triangle and perpendicular to the opposite side of the triangle
• Centroid: Point of intersection of the three median of the triangle is called the centroid of the triangle
• Isosceles Triangle Theorem: The angles opposite to the equal sides of an isosceles triangle are equal.
• Converse of Isosceles Triangle Theorem: The sides opposite to the equal angles of a triangle are equal.
• Angle-Side Relationship Theorem: In any triangle, the angle opposite to the longer side is larger.
• Converse of Angle-Side Relationship Theorem: In any triangle, the side opposite to the larger angle is longer.
• Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
• Pythagoras  theorem (right triangle with hypotenuse c): a² + b² = c² (where a, b, c are sides )
• Sum of angles: A + B + C = 180°  (where A, B, and C are angles of Triangle )