Pythagoras Theorem

In a right‑angled 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 other two sides. It is written as c² = a² + b², where c is the hypotenuse and a, b are the perpendicular sides.

Strengths

• Provides a quick way to find missing side lengths in right‑angled triangles.
• Fundamental for many topics: geometry, trigonometry, coordinate geometry, and real‑world measurements.
• Easy to remember and apply with simple arithmetic.

Weaknesses

• Only works for right‑angled triangles; cannot be used for acute or obtuse triangles directly.
• Requires accurate measurement; rounding errors can affect the result.

Opportunities

Example: A ladder leans against a wall. If the foot of the ladder is 3 m from the wall and the ladder reaches a height of 4 m, the length of the ladder (hypotenuse) is √(3² + 4²) = 5 m. This principle is used in construction, navigation, and designing ramps.

Threats

• Confusing the hypotenuse with one of the perpendicular sides.
• Applying the formula to non‑right triangles, leading to wrong answers.
• Forgetting to square the sides before adding them.

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Keywords: Pythagoras theorem, right triangle, hypotenuse, CBSE, ICSE, Class VIII, geometry, c² = a² + b²