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°).

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(9ab) + (5a²)(2b)
(8 x 9)(a x a x b) + (5 x 2)(a² x b)
(72)(a¹⁺¹ x b) + (10)(a²b)
72a²b + 10a²b
82a²b

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 7cm + 7cm + 14cm = 28cm

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 9 as well and sum (Inside, Outside) to equal -10. For this problem, those two numbers are -9 and -1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 10y + 9
y² + (-9 - 1)y + (-9 x -1)
(y - 9)(y - 1)

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 36° - 49° = 95°