Grade 9 Theorem of Pythagoras Quiz 1 draws its questions at random from 24 questions across these topics:
A few of the question types, with full solutions, so you know what to expect.
The hypotenuse. In a right-angled triangle, which side is the hypotenuse?
Answer: The side opposite the right angle
The hypotenuse is always OPPOSITE the right angle.
It is also the longest side of the triangle.
Tip: Find the little square in the corner, then look straight across from it. Never go by which side looks longest.
Stating the theorem. Complete the theorem: in a right-angled triangle, the square on the hypotenuse is equal to ...
Answer: the sum of the squares on the other two sides
In symbols: \(c^2 = a^2 + b^2\).
Tip: Squares, not the sides themselves. \(6 + 8\) is 14, but the hypotenuse of a 6-8 triangle is 10.
Finding the hypotenuse. A right-angled triangle has legs of 6 cm and 8 cm. Calculate the hypotenuse.
Answer: \(10\text{ cm}\)
\(c^2 = 6^2 + 8^2\)
\(c^2 = 36 + 64 = 100\)
\(c = \sqrt{100} = 10\)
Tip: You are finding the hypotenuse, so you ADD the squares.
Finding a shorter side. The hypotenuse of a right-angled triangle is 13 cm and one leg is 5 cm. Calculate the other leg.
Answer: \(12\text{ cm}\)
\(b^2 = 13^2 - 5^2\)
\(b^2 = 169 - 25 = 144\)
\(b = \sqrt{144} = 12\)
Tip: The hypotenuse was GIVEN, so you subtract. Adding here gives about 13,9 - longer than the hypotenuse, which is impossible.
Pythagorean triplets. Is 8; 15; 17 a Pythagorean triplet?
Answer: Yes, because \(64 + 225 = 289 = 17^2\)
\(8^2 + 15^2 = 64 + 225 = 289\)
\(17^2 = 289\)
Tip: Being whole numbers is not enough. 6; 8; 11 are all whole numbers and they do NOT form a triplet.