Pythagoras Theorem

Answer

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the remaining two sides. If c is the hypotenuse and a, b are the other two sides, then c² = a² + b².

Answer

A Pythagorean triplet is a set of three natural numbers where the square of the largest number equals the sum of squares of the other two numbers. Example: (3, 4, 5) because 5² = 3² + 4² → 25 = 9 + 16

Answer

If a and b are natural numbers and a > b, then [(a² + b²), (a² - b²), (2ab)] forms a Pythagorean triplet. For example, if a = 5 and b = 3: (34, 16, 30) is a Pythagorean triplet.

Answer

Side opposite to 30° = (1/2) × hypotenuse = (1/2) × 10 = 5 cm Side opposite to 60° = (√3/2) × hypotenuse = (√3/2) × 10 = 5√3 cm

Answer

Each equal side = (1/√2) × hypotenuse = (1/√2) × 6√2 = 6 cm Both perpendicular sides are equal to 6 cm each.

Answer

In a right-angled triangle, if an altitude is drawn to the hypotenuse, then the two triangles formed are similar to the original triangle and to each other. If △ABC has ∠B = 90° and BD ⊥ AC, then △ADB

Answer

In a right-angled triangle, the perpendicular from the right angle to the hypotenuse is the geometric mean of the segments into which it divides the hypotenuse. If QS ⊥ PR, then QS² = PS × SR.

Answer

In a triangle, if the square of one side is equal to the sum of the squares of the remaining two sides, then the triangle is a right-angled triangle. If c² = a² + b², then the triangle is right-angled