8.2. Converse of the Pythagorean Theorem http://www.ck12.org
4 ABCis an obtuse triangle.
Know What? RevisitedTo make the walls perpendicular, find the length of the diagonal.
652 + 722 =c^2
4225 + 5184 =c^2
9409 =c^2
97 =cIn order to make the building rectangular, both diagonals must be 97 feet.
Review Questions
- The twoshortersides of a triangle are 9 and 12.
a. What would be the length of the third side to make the triangle a right triangle?
b. What is a possible length of the third side to make the triangle acute?
c. What is a possible length of the third side to make the triangle obtuse? - The twolongersides of a triangle are 24 and 25.
a. What would be the length of the third side to make the triangle a right triangle?
b. What is a possible length of the third side to make the triangle acute?
c. What is a possible length of the third side to make the triangle obtuse? - The lengths of the sides of a triangle are 8x, 15 x,and 17x. Determine if the triangle is acute, right, or obtuse.
Determine if the following lengths make a right triangle.
- 15, 20, 25
- 20, 25, 30
- 8
√
3 , 6 , 2
√
39
Determine if the following triangles are acute, right or obtuse.
- 7, 8, 9
- 14, 48, 50
- 5, 12, 15
- 13, 84, 85
- 20, 20, 24
- 35, 40, 51
- 39, 80, 89
- 20, 21, 38
- 48, 55, 76
Graph each set of points and determine if 4 ABCis acute, right, or obtuse.
16.A( 3 ,− 5 ),B(− 5 ,− 8 ),C(− 2 , 7 )
17.A( 5 , 3 ),B( 2 ,− 7 ),C(− 1 , 5 )
18.WritingExplain the two different ways you can show that a triangle in the coordinate plane is a right triangle.