SSC CHSL 2021 Challenging Question | Geometry | Zero math | In English

SSC CHSL 2021 Challenging Question | Geometry | Zero math | In English
Triangles are fundamental shapes in geometry, and there are numerous theorems and properties associated with them. Here are some important theorems and properties related to triangles:\
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Triangle Sum Theorem: The sum of the three interior angles of a triangle is always equal to 180 degrees.
Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
Isosceles Triangle Theorem: In an isosceles triangle, the angles opposite the congruent sides are congruent.
Equilateral Triangle Theorem: In an equilateral triangle, all three angles are congruent, and each angle measures 60 degrees.
Pythagorean Theorem: In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is expressed as a^2 + b^2 = c^2, where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse.
Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, if a, b, and c are the lengths of the sides of a triangle, then a + b greater than c, a + c greater than b, and b + c greater than a.
Similar Triangles: Two triangles are similar if their corresponding angles are congruent, and their corresponding sides are proportional.
Angle Bisector Theorem: In a triangle, an angle bisector divides the opposite side into two segments that are proportional to the other two sides.
Median of a Triangle: The median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side. In an equilateral triangle, all medians are congruent and intersect at the centroid.
Altitude of a Triangle: The altitude of a triangle is a perpendicular line segment drawn from a vertex to the opposite side. The three altitudes of a triangle are concurrent (they intersect at a single point called the orthocenter).
Law of Sines: For any triangle with sides a, b, and c and opposite angles A, B, and C, the following relationship holds: sin(A)/a = sin(B)/b = sin(C)/c.
Law of Cosines: For any triangle with sides a, b, and c and angles A, B, and C, the following relationship holds: c^2 = a^2 + b^2 - 2ab * cos(C).
These theorems and properties are essential for solving various problems related to triangles and are foundational concepts in geometry. They help mathematicians and scientists understand and manipulate triangle shapes and dimensions in a wide range of applications.

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