Algebra Chapter 1: Tools of Algebra Lesson 1

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
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 a2 + b2 = c2, then the triangle is a
right triangle.
The Distance Formula:
The Distance Formula: The distance d
between any two points (x1, y1) and (x2, y2) is
d   x2  x1    y2  y1 
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 (x1, y1) and
(x2, y2) is  x1  x2 y1  y2 
Assignments and a note:
CW: Reteaching 11-2 and 11-3.
Homework 11-2: #3 - 21(every 3rd) and
11-3: #3-15 (every 3rd).
Concept Quiz on Thursday.

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