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.