Pythagorean Basics
The Pythagorean Theorem relates the sides of what type of triangle?
Right Triangle
A right triangle has legs measuring 3 units and 4 units. What is the length of the missing side?
5 or 5 units
What is the purpose of the Converse of the Pythagorean Theorem?
To prove if a triangle is a right triangle.
You walk 3 blocks east and 4 blocks north. How far are you from your starting point?
5 blocks
The Pythagorean Theorem can be extended to three dimensions to find this distance in a rectangular box.
The diagonal
What are the shorter sides of the right triangle called?
Legs
In a right triangle, if a=6 and b=8, what is c?
10
If a triangle has sides 5, 12, and 13, is it a right triangle?
Yes
A ladder is 10 feet long and reaches a window 8 feet above the ground. How far is the base of the ladder from the wall?
6 feet
What is different about finding the diagonal in a 3D shape?
You have to use the pythagorean theorem twice.
or
You have to use the diagonal formula.
The longest side of a right triangle is called what?
Hypotenuse
A right triangle has sides of 7 and 24. What is the hypotenuse?
25
Is a triangle with sides 9, 12, and 15 a right triangle?
Yes
A rectangular field is 60 meters long and 80 meters wide. What is the length of its diagonal?
100 meters
Find the space diagonal of a box with a length of 2, a width of 3, and a height of 6 units.
7 units
What is the formula for the Pythagorean Theorem?
a2+b2=c2
Given a right triangle with hypotenuse 15 and one leg 9, find the other leg.
12
A triangle has sides 8, 15, and 17. Is it a right triangle and how do you know?
It is because 82+152=172
or
It satisfies the converse of the pythagorean theorem
or
The sum of the squares of the legs equals the square of the hypotenuse
A television measures 32 inches diagonally and is 28 inches wide. How tall is it?
15.5 inches
A rectangular box has side lengths 5, 12, and 13. Find the length of the space diagonal.
18.4 or 18
What is the purpose of the Pythagorean Theorem?
To find the missing side of a right triangle.
The hypotenuse of a right triangle is 20.5 ft and the leg is 12.6 ft. What is the length of the missing side? Round to the nearest tenth.
16.2 ft
A triangle has sides with lengths of 68 meters, 25 meters, and 62 meters. Is it a right triangle? How do you know
No because it does not satisfy the converse of the pythagorean theorem
or
No because 622+252 does not equal 682
A ramp is 12 feet long and rises 5 feet. How far is the base of the ramp from the wall?
11 feet
A cube has sides of length 4. What is the length of its space diagonal? Round to the nearest tenth.
6.9