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.

Page 1: Introduction to Pythagorean Theorem

This page introduces the fundamental concepts of the Pythagorean theorem and its basic applications. The page demonstrates various examples of calculating missing sides in right triangles using the theorem's formula.

Definition: The Pythagorean theorem states that a² + b² = c², where c is the hypotenuse and a and b are the legs of a right triangle.

Highlight: The theorem only works for right triangles, and when finding the square root, only positive values are considered since length cannot be negative.

Example: A right triangle with legs of 3 and 4 units yields a hypotenuse of 5 units $3² + 4² = 5²$.

Vocabulary:

• Hypotenuse: The longest side of a right triangle, opposite to the right angle
• Legs: The two sides that form the right angle
• Pythagorean triples: Sets of three whole numbers that satisfy the Pythagorean theorem, like 3-4-5