Vocabulary
Hypotenuse
Legs
Distance Formula (Do in order from 100 to 500)
Converse of P. Theorem
100
What is the name of the formula a2+b2=c2
Pythagorean Theorem
100
Use the Pythagorean theorem to find c.
a = 3
b = 4
5
100
Use the Pythagorean theorem to find the missing leg for the triangle with c=5 and b=4.
a = 3
100
Determine the length of side A using any method.
3
100
Pythagoras' theorem states, "IF it is a right triangle, THEN a2+b2=c2." What is it's converse?
"IF a2+b2=c2, THEN it is a right triangle."
200
What type of triangles is Pythagorean Theorem used for?
Right Triangles
200
Use the Pythagorean theorem to find c.
a = 6
b= 8
10
200
Use the Pythagorean theorem to find the missing leg for the triangle with a= 8 and c=17.
b = 15
200
Determine the length of side B using any method.
4 units
200
Is this a right triangle? Justify mathematically.
82+62=102
64+36=100
100=100 ✅
Yes, this is a right triangle!
300
In the Pythagorean theorem, what are "a" and "b" called?
Legs
300
Use the Pythagorean theorem to find the missing hypotenuse for the triangle whose legs are 5 and 12.
13
300
Use the Pythagorean theorem to find the missing leg for the triangle with a = 7 and c = 25.
b = 24
300
Calculate the length of the hypotenuse (c).
25
300
Is a triangle with side lengths 12, 15, and 13 a right triangle? Justify mathematically.
No, it is not a right triangle because...
400
In the Pythagorean theorem, what is "c" called?
Hypotenuse
400
Use the Pythagorean theorem to find the missing hypotenuse for the triangle whose legs are 9 and 12.
15
400
Use the Pythagorean theorem to find the missing leg for the triangle with b=20 and c=29.
a = 21
400
Find the distance between points (0, 0) and (5, 12).
13 units
400
Describe the following triangle:
a = 4
b = 4
c = 10
Doesn't make a triangle
500
"This ancient Greek mathematician, often credited with the discovery of the theorem stating that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Pythagoras
500
Use the Pythagorean theorem to find the missing hypotenuse for the triangle whose legs are 12 and 16.
20
500
Use the Pythagorean theorem to find the missing leg for the triangle with c = 37 and b = 12.
a = 35
500
Calculate the distance between points (-5, -5) and (5, 5).
14.14 units
500
A commuter airline files a new route between two cities that are 400 kilometers apart. One of the two cities is 200 kilometers from a third city. The other one of the two cities is 300 kilometers from the third city. Do the paths between the three cities form a right triangle? Prove that your answer is correct.
No; 4002 = 160,000; 2002 + 3002 = 130,000