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°).

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

5a + 1 > \( \frac{a}{1} \)
1 x (5a + 1) > a
(1 x 5a) + (1 x 1) > a
5a + 1 > a
5a + 1 - a > 0
5a - a > -1
4a > -1
a > \( \frac{-1}{4} \)
a > -\(\frac{1}{4}\)

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-6a - 4z = 9a + z - 6
-6a = 9a + z - 6 + 4z
-6a - 9a = z - 6 + 4z
-15a = 5z - 6
a = \( \frac{5z - 6}{-15} \)
a = \( \frac{5z}{-15} \) + \( \frac{-6}{-15} \)
a = -\(\frac{1}{3}\)z + \(\frac{2}{5}\)