1. Warm Up
Use the figure for problems 1 and 2. round to the nearest hundredth
1) Find the height a of the triangle c 10 8 a 6 9
2) Find the length of side c
c =
c =
c =

2. Warm Up 5 units 6 units ??? B Find the distances between the points
C and D
E and F
A and B C
5 units A
6 units
??? F E D

3. The Pythagorean Thm and its Converse
Lesson 3-9
The Pythagorean Thm and its Converse
You'll Learn how to
Use the Distance formula and the converse of PYTH.THM

4. They form a right triangle They DO NOT form a right triangle
Use the converse of Pythagorean Theorem
The converse of the Pythagorean Theorem
If any positive numbers, a, b, and c satisfy the Pythagorean theorem a2 + b2 = c2 then a, b and c form a right triangle
EXAMPLE 1
Tell whether the given sides lengths form a right triangle.
i) 8, 15, 17
ii) 8, 10, 13
Checking
(c is the longest side)
Checking
(c is the longest side)
a2 + b2 = c2
a2 + b2 = c2 82 +
152 =
172 82 +
102 =
132 64 +
225 =
289 64 +
100 =
169
289 =
289
164 =
169
They form a right triangle
They DO NOT form a right triangle

5. Find the distance between the points.
Use the Distance Formula
EXAMPLE 1
Find the distance between the points.
Method1: Using Pythagorean Theorem B 5
c =
(4, 4)
x2, y2 3 c
c = A
(-1, 1)
c = 34
x1, y1
Method2: Using Distance Formula 4 -1 4 1 5 3 25 9 34

6. Find the distance between the points
EXAMPLE 2
Find the distance between the points
Using Distance Formula -4 -3 4 -3
(-4, 0)
x1, y1 16 9 25
(0, -3)
x2, y2

7. Lesson Quiz: Part I
Find the length of the diagonal of the rectangle.
1. width = 9 in., length = 40 in.
2. base length = 20 m, height = 15 m.

8. Lesson Quiz: Part II
Find the distance between the points to the nearest tenth.
3. Q and R
4. S and T

9. Lesson Quiz: Part III
Tell whether the given side lengths form a right triangle.
5. 12 cm, 13 cm, 16 cm no
6. 11 ft, 60 ft, 61 ft
yes

10. Lesson Quiz for Student Response Systems
1. Find the length of the diagonal of the rectangle.
width = 5 m, length = 12 m
A. 8 m
B. 11 m C. 13 m
D. 17 m 10 10

11. Lesson Quiz for Student Response Systems
2. Find the distance between the points to the nearest tenth.
Q and S
A. 6.0 m
B. 6.1 m C. 7.0 m
D m 11 11

12. Lesson Quiz for Student Response Systems
3. Tell whether the given side lengths form a right triangle.
12 ft, 13 ft, 14 ft
A. yes
B. no 12 12