7.2 converse of pythagorean theorem. remember: the hypotenuse of a triangle is the longest side
TRANSCRIPT
7.2 Converse of Pythagorean Theorem
7.2 Converse of Pythagorean Theorem
REMEMBER:The hypotenuse of a triangle is the longest side.
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.
ABC
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.
ABC
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.
ABC
Example 1Tell whether the triangle is a right
triangle. .
= 142 + 102 304 = 196 +
100
Not a right triangle
= 17.44c =
a =
= b
2)194(
304 = 296
222 bac
Example 2Tell whether the the given side lengths of
a triangle can represent a right triangle
= 72 + 142
245 = 49 + 196
Yes, a right triangle
= 15.65c a b 2)57(
245 = 245
222 bac
Example 3 aDecide 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
1:
Step 2:
c2 ? a2 +b2
24 + 30 = 54 30 + 39.34 = 69.34
So 54 > 39.34
= 39.34
So 69.34 > 24
24 + 39.34 = 63.34
So 63.34 > 30
? 242 + 302
2)436(1548 ? 576 + 9001548 ? 1476 so:1548 > 1476 so:The triangle is OBTUSEIs a triangle!
Example 3 bDecide 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
1:
Step 2:
c2 ? a2 +b2
8 + 10 = 18 10 + 12 = 22
So 18 > 12
So 22 > 8
8 + 12 = 20 So 20 > 10
122 ? 82 + 102
144 ? 64 + 100144 ? 164 so:
144 < 164 so:The triangle is ACUTEIs a triangle!
Example 4
8002 = 3052 + 7492
640,000 = 654,026
No, not directly north because it does not form a right triangle.
c = 800 ft
a = 305 ft
b = 749 ft 222 bac
In order to be directly north, there must be a RIGHT angle!
AssignmentSection 7.2 Pg 444;
1, 3-14, 16-21, 25-26, 29, 35, 36, 43