A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

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:

z² - 20z + 67 = -3z - 5
z² - 20z + 67 + 5 = -3z
z² - 20z + 3z + 72 = 0
z² - 17z + 72 = 0

Next, factor the quadratic equation:

z² - 17z + 72 = 0
(z - 8)(z - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 8) or (z - 9) must equal zero:

If (z - 8) = 0, z must equal 8
If (z - 9) = 0, z must equal 9

So the solution is that z = 8 or 9

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

The formula for circumference is circle diameter x π:

c = πd
c = 13π