A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

x² + 8x + 17 = -2x + 1
x² + 8x + 17 - 1 = -2x
x² + 8x + 2x + 16 = 0
x² + 10x + 16 = 0

Next, factor the quadratic equation:

x² + 10x + 16 = 0
(x + 2)(x + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 2) or (x + 8) must equal zero:

If (x + 2) = 0, x must equal -2
If (x + 8) = 0, x must equal -8

So the solution is that x = -2 or -8

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 2 x 9 = \( \frac{18}{2} \) = 9

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).