Triangles

Acute Triangle: All angles are less than 90 degrees.
Right Triangle: One angle is exactly 90 degrees.
Obtuse Triangle: One angle is greater than 90 degrees.
Isosceles Triangle: Two sides are equal in length.
Equilateral Triangle: All sides are equal in length.
Scalene Triangle: All sides are of different lengths.

===============

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry.

Theorem: The sum of the interior angles of a triangle is always 180 degrees.

Congruent Triangles: Two triangles are congruent if their corresponding sides and angles are equal.
Similar Triangles: Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Pythagorean Theorem: In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides. (c^2 = a^2 + b^2)
Sine Rule: In any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. (a/sin(A) = b/sin(B) = c/sin(C))
Cosine Rule: In any triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of those two sides and the cosine of the included angle. (c^2 = a^2 + b^2 - 2ab * cos(C))

Formula: The area of a triangle is equal to half the product of the base and the height. (A = 1/2 * b * h)
Heron's Formula: The area of a triangle can also be calculated using the lengths of its sides. (A = sqrt(s*(s-a)*(s-b)*(s-c)), where s = (a+b+c)/2)

Hypotenuse: The longest side of a right-angled triangle.
Base: The bottom side of a triangle.
Height: The perpendicular distance from the base of a triangle to its opposite vertex.

Angle Bisector: A line that divides an angle into two equal parts.
Median: A line that connects a vertex of a triangle to the midpoint of the opposite side.
Altitude: A line that connects a vertex of a triangle to the opposite side.

📐 Formula & Cheat Sheet (English)