Chapter 3 Test Review Honors Algebra 2

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: $$a^2 + b^2 = c^2$$ .

To find the length of a side in a right triangle, you can use the Pythagorean Theorem. If you know the lengths of the other two sides, you can rearrange the formula to solve for the unknown side.

The area (A) of a triangle can be calculated using the formula: $$A = \frac{1}{2} \times base \times height$$ .

A square root of a number x is a number y such that $$y^2 = x$$ . For example, the square root of 9 is 3, since $$3^2 = 9$$ .

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

A rational number can be expressed as a fraction $$\frac{a}{b}$$ where a and b are integers and b is not zero. An irrational number cannot be expressed as a simple fraction, and its decimal representation is non-repeating and non-terminating.

The expression $$\sqrt{a^2}$$ simplifies to |a|, which is the absolute value of a.

The quadratic formula is used to find the solutions of a quadratic equation of the form $$ax^2 + bx + c = 0$$ . It is given by: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

A relation is a set of ordered pairs, while a function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

The slope of a line measures its steepness and is calculated as the change in y divided by the change in x, often represented as $$m = \frac{\Delta y}{\Delta x}$$ .