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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 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 2 2 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 2 , 2 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.