Pythagoras Basics
What is Pythagoras’ theorem?
a2+b2=c2
Find the hypotenuse:
3, 4, ?
5
A student says:
32+42=12
What mistake did they make?
They added 3 and 4 instead of squaring first
Josh completes 4 laps of a 3 km track.
Distance travelled?
12 km
When finding the hypotenuse, do we:
Add the squares
What is the longest side of a right-angled triangle called?
Hypotenuse
Find the short side:
?, 12, 13
5
Miss Pollard says:
52+122=169
c=169
What did she forget?
Square root
A fishing rod costs $80 and is 25% off.
Discount amount?
$20
When finding a short side, do we:
Subtract the squares
What type of triangle can use Pythagoras’ theorem?
Right-angled triangle
Find the hypotenuse:
8, 15, ?
17
Phoenix solves:
x2+82=102
x2=164
What mistake did he make?
100−64 not plus
A rectangle has length 9 cm and width 5 cm.
Perimeter?
28 cm
A triangle has sides:
Which side is the hypotenuse?
13 cm
Which side is always labelled c?
Longest side / hypotenuse
Find the short side:
?, 24, 25
7
Why is the order important when finding the short side?
Must subtract smaller square from hypotenuse square / you will end up with a negative
A boat travels 6 km every hour.
How far in 5 hours?
30 km
Why can’t the hypotenuse be a smaller number than the other sides?
Because it is always the longest side
Why is the hypotenuse always the largest side?
Because it is opposite the largest angle (90°)
Find the hypotenuse:
9, 40, ?
41
Amaylia labels the shortest side as c.
Why is this incorrect?
c must be the hypotenuse
A campsite has 36 people.
Each tent fits 4 people.
How many tents are needed?
9
A triangle has sides:
Can this be a right-angled triangle? Explain.
No
Because:
62+82=100
√ 100=10
not 9.