Page 2: Advanced Applications

This page delves into more complex applications of the Pythagorean theorem, featuring challenging problems involving algebraic expressions and multiple steps.

Example: A complex problem involving the expression (3x)² + (15)² = (9 + 3x)², which demonstrates how the theorem can be used with variables.

Highlight: The page shows how to solve for unknown variables using the Pythagorean theorem in conjunction with algebraic manipulation.

Vocabulary:

• Algebraic expression: Mathematical statement using variables and constants
• Variable: A symbol representing an unknown value

Page 3: Real-World Applications

This page focuses on practical applications of the Pythagorean theorem in everyday scenarios and coordinate geometry.

Example: A sandwich cutting problem demonstrating how the theorem can be used to find diagonal lengths (30cm by 40cm sandwich with a 50cm diagonal).

Highlight: The page shows how to apply the theorem in coordinate geometry by finding distances between points.

Definition: In coordinate geometry, the distance between two points can be found by treating the horizontal and vertical distances as legs of a right triangle.

Example: Finding the distance between points (4,7) and (16,12) using the Pythagorean theorem, resulting in 13 units.