Flashcards · Maths · Geometry and Measures
Pythagoras' Theorem
-
What is Pythagoras' theorem?
\(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse.
-
What is the hypotenuse?
The longest side of a right-angled triangle, opposite the right angle.
-
How do you find the hypotenuse?
Square the two shorter sides, add them, then take the square root.
-
How do you find a shorter side?
Square the hypotenuse, subtract the square of the other side, then take the square root.
-
What is a Pythagorean triple?
Three whole numbers that satisfy \(a^2 + b^2 = c^2\).
-
Name four Pythagorean triples.
\(3, 4, 5\), \(5, 12, 13\), \(8, 15, 17\) and \(7, 24, 25\).
-
What is the hypotenuse for shorter sides 6 cm and 8 cm?
10 cm.
-
What is the hypotenuse for shorter sides 9 cm and 12 cm?
15 cm.
-
How can you test if a triangle is right-angled?
Check whether \(a^2 + b^2 = c^2\) for the longest side \(c\).
-
How do you find the height of an isosceles triangle?
Split it down the middle and use Pythagoras with half the base.
-
What is the height of an isosceles triangle with base 10 cm and sides 13 cm?
12 cm.
-
Which triangle do you use to find the diagonal of a rectangle?
The right-angled triangle made by the length, the width and the diagonal.
-
What is the size of a shorter side if the hypotenuse is 13 and the other side is 5?
12.
-
What is \(\sqrt{20}\) in simplest surd form (Higher tier)?
\(2\sqrt{5}\).
-
How do you find the distance between two points on a grid (Higher tier)?
Use the horizontal and vertical differences as the two shorter sides of a right-angled triangle.
-
How do you find the diagonal of a cuboid (Higher tier)?
Use Pythagoras twice.