Section 11.6
Pythagorean Theorem and Distance Formula
Name
Period #
The Pythagorean Theorem
In a right triangle, the sum of the squares of the lengths of the legs (a and b) is
equal to the square of the length of the hypotenuse (c).
FORMULA:
a2  b2  c2
 c is always the ____________________________
Refer to the triangle above. Find the missing side length. Leave all answers in simplified ROOT FORM.
1. a  12 , b  16 , c  ______.
2. a  7 , b  4 , c  ______.
3. a  ______, b  10 , c  16 .
4. a  40 , b  ______, c  41 .
5. a  b  16 , c  ______.
6. a  b  9 , c  ______.
7. a 
1
b , b  8 , c  ______.
2
1
8. a  12 , b  a , c  ______.
3
CONVERSE of the Pythagorean Theorem:
If the sum of the squares of the ___________ of a triangle, is equal to the square of the ____________________
then the sides form a right triangle.
State whether or not the three given numbers represent the lengths of the sides of a right triangle.
9. 9, 16, 20 ______
10. 9, 40, 41 ______
11. 9, 12, 15 ______
12. 5, 6, 7 ______
13. 6, 8, 10 ______
14. 17, 18, 33______
Using the following formula, you can find a formula for the distance between any two points on the
coordinate plane:
THE DISTANCE FORMULA
The distance d between points (x1, y1) and (x2, y2) is given by:
d 
( x2  x1 ) 2  ( y 2  y1 ) 2
MEMORIZE IT!!!!!
Find the distance between the given points on the coordinate plane. Write the answer in simplest radical
form!
15. (-4, 2) and (2, -1)
16. (-2, -3) and (-2, 4)
17.
18. (-1, 8), (5, -3)
(6, 0), (5, 1)
11.6 Homework Worksheet
Name
Period #
Use the distance formula to find the distance between the given pair of points. Answers in ROOT form!!!
1. (-6, 0) and (4, 0)
2. (3, 4) and (9, 7)
3. (-4, 7) and (-9, -5)
4. (4, -4) and (9, -8)
5. (3, -7) and (12, -8)
6. (-2, 1) and (-8, -5)
Use Pythagorean Theorem to find the missing side length of the triangle given below if a and b are the
length of the legs and c is the length of the hypotenuse of the triangle. Leave answers in ROOT form!!!
7. a  5 , b =______, c  15 .
8. a  ______, b  16 , c  24 .
9. a  5 , b  5 , c  ______.
10. a  ______, b  3 , c  6 .
State whether the three given lengths could be the sides of a right triangle.
11. 4, 7, and 9
13.
_____________
2 , 2, and 5 _____________
12. 20, 21, and 29
_____________
14. 8, 15, and 17
_____________
Find the missing variable to the nearest tenth if necessary.
15.
16.
c in
5 in
12 ft
n ft
11 in
6 ft
17. Anna’s desk faces a corner of her rectangular room. If the desk is 51 inches long, and one side is about 36
inches from the corner, how far is the other side from the corner? Round your answer to the nearest tenth.