Algebra 1B Chapter 11: Radical Expressions and Equations Lesson 11-2: The Pythagorean Theorem Lesson 11-3:The Distance and Midpoint Formulas

Goals: Solve problems using the Pythagorean Theorem.

Identify right triangles.

Find the distance between two points on a coordinate plane.

Find the coordinates of the midpoint of a line segment.

Radical Expressions



radical expression

: A radical expression is an expression that contains a radical sign.

Simplest Radical Form:

 A radical expression is in simplest radical form when all three statements are true.

   The radicand has no perfect-square factors other than 1.

The radicand has no fractions.

The denominator of a fraction has no radicals.

Right triangles:

 A right triangle contains a right angle (a 90º angle). The side opposite the right angle is the

hypotenuse

. It is the longest side. Each of the sides forming the right angle is a

leg

.

The Pythagorean Theorem:



The Pythagorean Theorem

: In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.



The Converse of the Pythagorean Theorem

: If a triangle has sides of lengths a, b, and c, and a 2 + b 2 = c 2 , then the triangle is a right triangle.

The Distance Formula:



The Distance Formula

: The distance d between any two points (x 1 , y 1 ) and (x 2 , y 2 ) is

d

 

x

2 

x

1

y

2 

y

1  2

The Midpoint Formula:



Midpoint

: The midpoint of AB is the point M that divides the segment into two equal segments, so that AM = MB.



The Midpoint Formula

: The midpoint M of a line segment with endpoints (x 1 , y 1 ) and (x 2 , y 2 ) is

x

1  2 ,  2

y

2

Assignments and a note:

 CW: Reteaching 11-2 and 11-3.

 Homework 11-2: #3 - 21(every 3 rd ) and 11-3: #3-15 (every 3 rd ).

 Concept Quiz on Thursday.