1. 7.2 Converse of Pythagorean Theorem

2. REMEMBER:
The hypotenuse of a triangle is the longest side.

3. Theorems: Theorem 7.2: 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 2 sides, then the triangle is a RIGHT triangle.
In General: If c2 = a2 + b2 then is a RIGHT triangle.

4. Theorems:
Theorem 7.3:
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other 2 sides, then the triangle is an ACUTE triangle.
In General: If c2 < a2 + b2 then is an ACUTE triangle.

5. Theorems:
Theorem 7.4:
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other 2 sides, then the triangle is an OBTUSE triangle.
In General: If c2 > a2 + b2 then is an OBTUSE triangle.

6. Example 1 Tell whether the triangle is a right triangle. . = 17.44
c = =
a =
= b
304 =
304 = 296
Not a right triangle

7. Example 2
Tell whether the the given side lengths of a triangle can represent a right triangle a b c =
= 15.65
245 =
245 = 245
Yes, a right triangle

8. Example 3 a
Decide if the segment lengths form a triangle. If so, would the triangle be acute, obtuse, or right?
Must use Triangle Inequality Theorem to check the segments can make a triangle.
= 39.34
Step 2:
c2 ? a2 +b2
Step 1: ?
= 54
So 54 > 39.34
1548 ?
1548 ? so:
= 69.34
So > 24
1548 > so:
= 63.34
So > 30
The triangle is OBTUSE
Is a triangle!

9. Example 3 b
Decide if the segment lengths form a triangle. If so, would the triangle be acute, obtuse, or right?
Must use Triangle Inequality Theorem to check the segments can make a triangle.
Step 2:
c2 ? a2 +b2
Step 1:
122 ?
= 18
So 18 > 12
144 ?
144 ? so:
= 22
So 22 > 8
144 < 164 so:
= 20
So 20 > 10
The triangle is ACUTE
Is a triangle!

10. Example 4 In order to be directly north, there must be a RIGHT angle!
a = 305 ft
b = 749 ft
c = 800 ft
8002 =
640,000 = 654,026
No, not directly north because it does not form a right triangle.

11. Assignment
Section 7.2 Pg 444;
1, 3-14, 16-21,
25-26, 29, 35, 36, 43