Pythagoras Theorem Flashcards

All 6 cards in this deck

What is Pythagoras' theorem?

$a^2 + b^2 = c^2$
$c$ is the hypotenuse (longest side, opposite the right angle); $a$ and $b$ are the two shorter sides.

What are the steps to find the hypotenuse of a right-angled triangle?

e.g. shorter sides 6 cm and 8 cm

1. Square both shorter sides: $6^2 = 36$, $8^2 = 64$
2. Add them: $36 + 64 = 100$
3. Square root: $c = \sqrt{100} = 10$ cm

True or false? If you know the hypotenuse and one shorter side, you find the other shorter side by subtracting the squares.

True.
e.g. hypotenuse 8.5, shorter side 4: $8.5^2 - 4^2 = 56.25$, so the side is $7.5$.

How do you test whether a triangle is right-angled using Pythagoras' theorem?

e.g. sides 9 cm, 12 cm, 15 cm

Square the two shorter sides, add, and check it equals the square of the longest side.
$9^2 + 12^2 = 225 = 15^2$, so it is right-angled.

What are the steps to find the distance between two points on a coordinate grid?

e.g. $(-1, 1)$ and $(3, 4)$

1. Find the difference in $x$ and in $y$: $4$ and $3$
2. Square and add: $16 + 9 = 25$
3. Square root: distance $= \sqrt{25} = 5$

What are the steps to find the perpendicular height of an equilateral triangle, leaving the answer in surd form?

e.g. side 8 cm

1. Split it into two right-angled triangles: base $= 4$, hypotenuse $= 8$
2. Pythagoras: $h^2 = 8^2 - 4^2 = 48$
3. $h = \sqrt{48} = 4\sqrt{3}$ cm