1. ESSENTIAL QUESTION: What kind of triangle is there when c2 is not equal to a2 + b2

2. The Converse of the Pythagorean Theorem
If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

3. Is ∆ABC a right triangle?
Example 1
Verify a Right Triangle
Is ∆ABC a right triangle?
SOLUTION
Compare c2 with a2 + b2.
c2 a2 + b2 ? =
Substitute 20 for c, 12 for a, and 16 for b. ? =
Multiply. ? =
400 = 400
Simplify.
ANSWER
It is true that c2 = a2 + b2. So, ∆ABC is a right triangle. 3

4. c2 = a2 + b2 RIGHT c2 > a2 + b2 OBTUSE c2 < a2 + b2 ACUTE
Right Triangle????
c2 = a2 + b2 RIGHT
c2 > a2 + b2 OBTUSE
c2 < a2 + b2 ACUTE

5. I DO…. Example 2 Show that the triangle is an acute triangle. SOLUTION
Compare the side lengths.
Compare c2 with a2 + b2.
c2 a2 + b2 ? =
Substitute for c, 4 for a, and 5 for b. 35 ? =
Multiply. ? =
35 < 41
Simplify.
ANSWER
Because c2 < a2 + b2, the triangle is acute. 5

6. I DO…. Example 3 Show that the triangle is an obtuse triangle.
SOLUTION
Compare the side lengths.
c2 a2 + b2 ? =
Multiply. ? =
225 > 208
Simplify.
ANSWER
Because c2 > a2 + b2, the triangle is obtuse. 6

7. WE DO…. Example 4 Classify the triangle as acute, right, or obtuse.
SOLUTION
c2 a2 + b2 ? = ? =
Multiply. ? =
64 > 61
Simplify.
ANSWER
Because c2 > a2 + b2, the triangle is obtuse. 7

8. Example 5
WE DO.…
Classify the triangle with the given side lengths as acute, right, or obtuse. a.
4, 6, 7 b.
12, 35, 37
SOLUTION a.
c2 a2 + b2 ? = b.
c2 a2 + b2 ? = ? = ? = ? = ? =
49 < 52
1369 = 1369
The triangle is acute.
The triangle is right. 8

9. Checkpoint
YOU DO….
Classify the triangle as acute, right, or obtuse. Explain. 1. 2. 3.

10. Classify the triangle as acute, right, or obtuse. Explain.
Checkpoint
Classify Triangles
Classify the triangle as acute, right, or obtuse. Explain. 1.
ANSWER
obtuse; 62 > 2.
ANSWER
right; 172 = 3.
ANSWER
acute; 72 <

11. Checkpoint
Classify Triangles
Use the side lengths to classify the triangle as acute, right, or obtuse. 4.
7, 24, 24 5.
7, 24, 25 6.
7, 24, 26

12. Checkpoint
Classify Triangles
Use the side lengths to classify the triangle as acute, right, or obtuse. 4.
7, 24, 24
ANSWER
acute 5.
7, 24, 25
ANSWER
right 6.
7, 24, 26
ANSWER
obtuse

13. Hw Practice 4.5B