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ICSE Class 9 Geometry: Pythagoras theorem — practice questions

Explore 28 free Geometry: Pythagoras theorem questions in ICSE Class 9 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Geometry: Pythagoras theorem questions and exercises with answers

Showing questions 1–28 of 28.

Pythagoras's theorem relates the sides of which geometric shape?Read the answer and worked solution →Which name specifies the boundary segment facing the 90-degree corner?Read the answer and worked solution →If side lengths of a triangle satisfy a² + b² = c², what is true?Read the answer and worked solution →When c is the longest side and a² + b² > c², the triangle is:Read the answer and worked solution →For longest side c, which condition makes a triangle obtuse?Read the answer and worked solution →Which proposition of Euclid's Elements Book I contains the converse?Read the answer and worked solution →Which Babylonian tablet from c. 1800 BC lists Pythagorean triples?Read the answer and worked solution →The ancient tablet YBC 7289 calculates the diagonal of which shape?Read the answer and worked solution →Which ancient Indian text stated Pythagoras's theorem?Read the answer and worked solution →In classical Chinese mathematics, Pythagoras's theorem is called:Read the answer and worked solution →Which Chinese mathematical text reasoned the (3, 4, 5) triangle?Read the answer and worked solution →Pythagoras's rule yields a leg and hypotenuse differing by how much?Read the answer and worked solution →Dropping an altitude to the hypotenuse creates triangles that are:Read the answer and worked solution →In the rearrangement proof, what is the combined area of 4 right triangles?Read the answer and worked solution →What is a set of three positive integers satisfying a² + b² = c² called?Read the answer and worked solution →What is the greatest common divisor of a primitive Pythagorean triple?Read the answer and worked solution →In Euclid's formula for Pythagorean triples with m > n, hypotenuse c is:Read the answer and worked solution →Euclid's formula yields a primitive triple if m and n are coprime and:Read the answer and worked solution →In every primitive Pythagorean triple, what parity does hypotenuse c have?Read the answer and worked solution →In a primitive triple (a, b, c), which member is always divisible by 4?Read the answer and worked solution →What is the largest integer that always divides the product abc?Read the answer and worked solution →The integer area of any Pythagorean triangle is always divisible by:Read the answer and worked solution →Can the acute angles of a Pythagorean triangle have rational degrees?Read the answer and worked solution →Which coordinate geometry formula derives from Pythagoras's theorem?Read the answer and worked solution →Match each right-triangle property with the Pythagorean principle:Read the answer and worked solution →Match each pair of legs with the computed hypotenuse:Read the answer and worked solution →Match each geometric figure with its diagonal calculated via Pythagoras:Read the answer and worked solution →Match each triangle classification based on side lengths (a ≤ b < c):Read the answer and worked solution →

Worked practice questions

Pythagoras's theorem relates the sides of which geometric shape?

  1. A right triangle
  2. An acute triangle
  3. An obtuse triangle
  4. A scalene triangle
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Correct answer: A. A right triangle

Pythagoras's theorem applies specifically to the sides of a right triangle.

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Which name specifies the boundary segment facing the 90-degree corner?

  1. The altitude
  2. The hypotenuse
  3. The perimeter
  4. The median line
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Correct answer: B. The hypotenuse

The side lying directly opposite the right angle is termed the hypotenuse.

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If side lengths of a triangle satisfy a² + b² = c², what is true?

  1. The triangle is acute
  2. The triangle is obtuse
  3. It is a right triangle
  4. It is an equilateral
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Correct answer: C. It is a right triangle

By the converse theorem, satisfying a² + b² = c² means the triangle is a right triangle.

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More Mathematics topics

Coordinate GeometryAlgebra: expansionsAlgebra: factorisationAlgebra: logarithmsGeometry: triangles (congruency, mid-point theorem)MensurationPythagoras TheoremAlgebra: indices