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°).

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(4 + 2)(2)
a = ½(6)(2)
a = ½(12) = \( \frac{12}{2} \)
a = 6

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.

b - 6 < \( \frac{b}{4} \)
4 x (b - 6) < b
(4 x b) + (4 x -6) < b
4b - 24 < b
4b - 24 - b < 0
4b - b < 24
3b < 24
b < \( \frac{24}{3} \)
b < 8

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 31° - 39° = 110°

A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.