Special Right Triangles: Key Relationships and Calculations

The first page introduces two fundamental special right triangles: the 45-45-90 and 30-60-90 triangles, along with their essential properties and calculations. These triangles have unique characteristics that make them particularly useful in geometric problem-solving.

Definition: A 45-45-90 triangle is a right triangle with two 45-degree angles and one 90-degree angle, where both legs are equal in length.

Highlight: For a 45-45-90 triangle, if the legs are length x, the hypotenuse will always be x√2.

Example: In a 45-45-90 triangle with legs of 5 units, the hypotenuse would be 5√2 ≈ 7.1 units.

Vocabulary: The "leg" refers to either of the two sides that form the right angle in a right triangle, while the "hypotenuse" is the longest side opposite the right angle.

Definition: A 30-60-90 triangle has angles of 30, 60, and 90 degrees, with sides following a specific ratio pattern.

Example: In a 30-60-90 triangle with a short leg of 14 units, the long leg would be 14√3 ≈ 24.2 units, and the hypotenuse would be 28 units.

Highlight: For a 30-60-90 triangle, if the shortest leg is x, then the long leg is x√3, and the hypotenuse is 2x.