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 entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

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, \(c = \sqrt{a + b}\)

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.

3x + 7 < \( \frac{x}{1} \)
1 x (3x + 7) < x
(1 x 3x) + (1 x 7) < x
3x + 7 < x
3x + 7 - x < 0
3x - x < -7
2x < -7
x < \( \frac{-7}{2} \)
x < -3\(\frac{1}{2}\)

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

p = x + y + z
p = 10cm + 11cm + 12cm = 33cm