9.3 converse of a pythagorean theorem classifying triangles by their sides
TRANSCRIPT
9.3 Converse of a Pythagorean Theorem
Classifying Triangles by their sides
Converse of the Pythagorean Theorem
If the square of the longest side is equal to the sum of the squares of the other sides then the triangle is a Right triangle.
Theorem
If c2 is less then a2 + b2, then the triangle is Acute
222 cba
a
b
c
Theorem
If c2 is greater then a2 + b2, then the triangle is Obtuse
222 cba
a
b
c
The Gift Wrapping Principle
If you are trying to find out what type of triangle can be made from the given sides and the smaller sides sum is not greater then the largest side, then a triangle can not be made.
Do you remember going over this around Christmas?
What type of Triangle
Sides
4.13,10,7
What type of Triangle
Sides
Obtuse
4.13,10,7
What type of Triangle
Sides
12,56,6
4.13,10,7 Obtuse
What type of Triangle
Sides
Right
Obtuse
12,56,6
4.13,10,7
What type of Triangle
Sides
2,3,1
12,56,6
4.13,10,7
Right
Obtuse
What type of Triangle
Sides
Right
Right
Obtuse
2,3,1
12,56,6
4.13,10,7
What type of Triangle
Sides
12 7, ,4
2,3,1
12,56,6
4.13,10,7
Right
Right
Obtuse
What type of Triangle
Sides
PossibleNot 12 7, ,4
2,3,1
12,56,6
4.13,10,7
Right
Right
Obtuse
Homework
Page 546 – 549
# 8 – 25, 26, 28,
36, 37, 40,
47 - 54