Pythagorean Theorem, Pythagorean Converse, Special Right Triangles

10

10√3

10√2

20

22

11√3

11√2

11

a

b

c

d

22 in

23 in

24 in

25 in

acute

obtuse

right

left

Because a 45, 45, 90 triangle is scalene.

Because a 45, 45, 90 triangle is isosceles.

Because a 45, 45, 90 triangle is equilateral.

Because a 45, 45, 90 triangle is obtuse.

x= 20, y=20

x=20, y= 20 $$\sqrt{2}$$

x= 20 $$\sqrt{2}$$ , y= 20

x= 20, y=45

x=4, y=4

x=4, y=8

x=8, y=4

x=8, y=8 $$\sqrt{3}$$

Pythagorean Theorem

Converse of the Pythagorean Theorem

45, 45, 90 Triangle Theorem

30, 60, 90 Triangle Theorem

If the square of the longest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.

If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is a right triangle.

If the square of the longest side of a triangle is more than the sum of the squares of the other two sides, then the triangle is a right triangle.

None of the above.