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Goals : Solve problems using the Pythagorean Theorem. Identify right triangles.

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.

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Goals : Solve problems using the Pythagorean Theorem. Identify right triangles.

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  1. Algebra 1BChapter 11: Radical Expressions and EquationsLesson 11-2: The Pythagorean TheoremLesson 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.

  2. Radical Expressions • radical expression: A radical expression is an expression that contains a radical sign.

  3. 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.

  4. 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.

  5. 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.

  6. The Distance Formula: • The Distance Formula: The distance d between any two points (x1, y1) and (x2, y2) is

  7. 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

  8. 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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