Page 571 - Algebra 1

L E S S O N Solving Problems Using the Pythagorean
85
Theorem
Warm Up
1. Vocabulary The square of an integer is a (perfect square,
(13)
radical expression). Simplify.
2. √ 62 5 3. √ 19 6 (13) (13)
Estimate to the nearest tenth. 5. √ 38 9
(13)
4. √ 21 6 (61)
New Concepts The Pythagorean Theorem states an important relationship among the lengths of the sides of any right triangle.
Pythagorean Theorem
If a triangle is a right triangle with legs of lengths a and b and hypotenuse of length c, then
a2 +b2 =c2.
a
c b
Math Language
The hypotenuse of a right triangle is the side opposite the right angle. The legs are the sides that form the right angle.
Exploration Justifying the Pythagorean Theorem
The legs of the four blue congruent triangles form a square. The gray
c
Online Connection www.SaxonMathResources.com
1. Explain why (a + b)2 represents the area of the outer square formed by the blue triangles.
2. What area does the expression _1 ab represent? 2
3. Write an algebraic expression for the area of the gray square.
4. Use the expressions from problems 1, 2, and 3 to translate the statement
below into an equation.
Area of outer square = Area of 4 triangles + Area of gray square
5. Show that the equation you wrote in problem 4 simplifies to a2 +b2 =c2.
quadrilateral is also a square.
a
ba
b
b
ab
a
556 Saxon Algebra 1