Pythagoras Theorem Flashcards

All 6 cards in this deck

What is Pythagoras' theorem?

$a^2 + b^2 = c^2$, where $c$ is the hypotenuse and $a$, $b$ 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: $\sqrt{100} = 10$ cm

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

e.g. hypotenuse $13$ cm, one shorter side $5$ cm

1. Square both known sides: $13^2 = 169$, $5^2 = 25$
2. Subtract from the hypotenuse squared: $169 - 25 = 144$
3. Square root: $\sqrt{144} = 12$ cm

True or false? To find a shorter side of a right-angled triangle you add the squares of the other two sides.

False. You subtract: shorter side $= \sqrt{\text{hyp}^2 - \text{other side}^2}$.

How do you test whether a triangle with three given sides is right-angled?

e.g. sides $5$ cm, $12$ cm, $13$ cm

Check whether the squares of the two shorter sides add to the square of the longest side: $25 + 144 = 169 = 13^2$, so it is right-angled.

A straight ladder leans against a vertical wall. In the right-angled triangle formed by the ladder, the wall and the ground, which side is the hypotenuse?

The ladder. It is opposite the right angle between the wall and the ground, so it is the longest side.