1. Pythagorean Theorem, its Converse and the coordinate system
Objective:
Students will use the Pythagorean theorem
and its converse.

2. Algebra Standards:
2.0 Students understand and use such operations as taking
the opposite, reciprocal, raising to a power, and
taking a root. This includes the understanding and use of
the rules of exponents.

3. Vocabulary: For Right Triangles Only! c b a Pythagorean Theorem c b a
hypotenuse
- always opposite
the right angle c
leg b a
Pythagorean Theorem
leg a2 + b2 = c2
hypotenuse c b a a b

4. Pythagorean Theorem Pythagorean Theorem 2 a) b) 5 5 12 a2 + b2 = c2 a2
#1 Use the Pythagorean the square
Find the missing side. 2 a) b) 5 5
Pythagorean Theorem 12
Pythagorean Theorem a2 + b2 = c2 a2 + b2 = c2 22 + 52 = x2 52 +
122 = x2 4 + 25 = x2 25 +
144 = x2 29 = x2
169 = x2 29 =
|x| 13 =
|x| x =
29 or -29 x =
13 or -13

5. Pythagorean Theorem Pythagorean Theorem 3 c) d) 5 3 7 a2 + b2 = c2 a2
#1 Use the Pythagorean the square
Find the missing side. 3 c) d) 5 3 7
Pythagorean Theorem
Pythagorean Theorem a2 + b2 = c2 a2 + b2 = c2 32 + x2 = 72 32 + x2 = 52 9 + x2 = 49 9 + x2 = 25
– 9 –9
– 9 –9 x2 = 40 x2 = 16
|x| = 40 =
2 10
|x| = 4 x = or x =
4 or -4

6. Pythagorean Theorem 10 a2 + b2 = c2 x x2 + (x+2)2 = 102 x x2
#2 Use the Pythagorean the square
A right triangle has one leg that is 2 inches longer that the
other leg. The hypotenuse is 10 inches. Find the
unknown legs.
Pythagorean Theorem 10 a2 + b2 = c2 x x2 +
(x+2)2 =
102 x x2
+ x2 + 4x + 4 =
100
+ 2
2x2
+ 4x
– 96 = 2 x = 6 or
– 8 x2
+ 2x
– 48 =
Leg one = 6
Leg two = 8
( )( ) x – 6 x + 8 =

7. Pythagorean Theorem 15 a2 + b2 = c2 x x2 + (x+3)2 = 152 x x2
#3 Use the Pythagorean the square
A right triangle has one leg that is 3 inches longer that the
other leg. The hypotenuse is 15 inches. Find the
unknown legs.
Pythagorean Theorem 15 a2 + b2 = c2 x x2 +
(x+3)2 =
152 x x2
+ x2 + 6x + 9 =
225
+ 3
2x2
+ 6x
– 216 = 2 x = 9 or
– 12 x2
+ 3x
– 108 =
Leg one = 9
Leg two = 12
( )( ) x – 9 x + 12 =

8. Pythagorean Theorem 2 a2 + b2 = c2 22 + 22 = x2 2 4 + 4 = x2 8 = x2 2
#4 Use the Pythagorean the square
A board game is a square 2 ft by 2ft. What is the length
of the diagonal?
Pythagorean Theorem 2 a2 + b2 = c2 22 + 22 = x2 2 4 + 4 = x2 8 = x2 2
2 2 =
|x| 2 x =
2 2 or

9. Determine whether the given lengths could
#5 Converse of the Pythagorean Theorem
Determine whether the given lengths could
be the sides of a right triangle. 1) 2) a2 + b2 = c2 a2 + b2 = c2 52 +
122 =
132 92 + 62 =
122 25 +
144 =
169 81 + 36 =
144
169 =
169
117 =
144
yes no

10. A car drives 20 miles due east and then 45 miles
Real world Application
A car drives 20 miles due east and then 45 miles
due south. To the nearest hundredth of a mile,
how far is the car from its starting point? a2 + b2 = c2
20 miles
202 +
452 = x2
400 +
2025 = x2 x
45 miles
2425 = x2 =
|x| x
= or

11. Real world Application

12. Real world Application

13. Pythagorean Theorem and the Coordinate Plane
Standard:
8.G8 – Apply the Pythagorean Theorem to find the distance
Between two points in a coordinate system

14. Using Coordinates

16. Find the distance between the two points.
Point A (-5, -6) and Point B (-2, 4)