Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’

Lesson 10.1Lesson 10.1The Pythagorean TheoremThe Pythagorean Theorem

The Pythagorean Theorem

• The side opposite the right angle is called the hypotenuse.

• The other two sides are called legs.

• We use ‘a’ and ‘b’ to represent the legs and ‘c’ to represent the hypotenuse.

a

b

c

The Pythagorean Theorem

C-88: Pythagorean Theorem - In a right triangle, if a and b are lengths of the legs and c is the length of the hypotenuse, then .

a2 +b2 =c2

a a

b

b

c

c

Lesson 10.2Lesson 10.2Converse of the Pythagorean TheoremConverse of the Pythagorean Theorem

Pythagorean Triples

• Pythagorean Triple: three positive integers that work in the Pythagorean Formula.

• Some popular sets are: 3,4,5 5,12,13, 6,8,10...

Pythagorean Triples

C-89: Converse of the Pythagorean Theorem - If the lengths of the three

sides of a triangle work in the Pythagorean formula, then the triangle is a right

triangle.

Let’s test the side lengths of this triangle and determine if it is

indeed a right triangle.

82 +152 =172 ?64 + 225 =289? 289 =289Since the lengths of the sides when used in the

Pythagorean Formula show that both sides of the

equation are equal we can conclude these side

lengths are those of a right triangle.