This last postulate cannot be proven as a theorem. In non-Euclidean geometry, this “parallel” postulate does not hold true.

A single line always has a measure of 180°. Two lines are parallel if they have the same slope and never intersect. Perpendicular lines are two lines that come together to form a 90° angle. Intersecting lines are any two lines that cross each other at any point. Parallel lines can never intersect, but perpendicular lines can.

Being able to identify the various types of angles is an essential part to understanding geometry. Two lines that make a right angle are also perpendicular to each other. They form a perfect corner. You may also see a straight angle which is simply a line. The measure of this angle is 180°. For example: A square or rectangle has four 90° angles while a circle has no angles.

Equilateral triangles have three equal sides and three angles that all measure exactly 60°. Isosceles triangles have two equal sides and two equal angles. Scalene triangles have no equal sides and no equal angles.

The perimeter of a circle is called the circumference and is equal to 2πr where “r” is the radius. The area of a circle is πr2 where “r” is the radius. The perimeter of a rectangle is 2l + 2w where “l” is the length and “w” is the width. The area of a rectangle is l x w where “l” is the length and “w” is the width. The perimeter of a triangle is a + b + c where each variable denotes one side of the triangle. The area of a triangle is ½bh where “b” is the base of the triangle and “h” is the vertical height.

The surface area of a sphere is equal to 4πr2, where “r” is the radius of the sphere. The volume of a sphere is equal to (4/3)πr3, where “r” is the radius of the sphere. The surface area of a rectangular prism is 2lw + 2lh + 2hw, where “l” is the length, “w” is the width, and “h” is the height. [14] X Research source The volume of the rectangular prism is l x w x h, where “l” is the length, “w” is the width, and “h” is the height. [15] X Research source

Angle pairs are equal to each other if two of the lines are parallel. [20] X Research source There is a fourth angle pair: consecutive interior angles. These are the two angles on the inside of the lines and on the same side of the transversal. When the two lines are parallel, the consecutive interior angles always add up to 180°. [21] X Research source

For example: If you have a right triangle with side a = 3 and b = 4, you can find the hypotenuse: a2 + b2 = c2 32 + 42 = c2 9 + 16 = c2 25 = c2 c = √25 c = 25; the hypotenuse of the triangle is 5.

Label all of the unknowns as well. A clearly drawn diagram is the easiest way to understand the problem.

For example: Angle ABC and angle DBE make a line, ABE. Angle ABC = 120°. What is the measure of angle DBE? Since the sum of angle ABC and DBE must equal 180°, then angle DBE = 180° - angle ABC. Angle DBE = 180° - 120° = 60°.

The reflexive property: A variable is equal to itself. x = x. The addition postulate: When equal variables are added to equal variables, all of the sums are equal. A + B + C = A + C + B. The subtraction postulate: This is similar to the addition postulate, all variables subtracted from equal variables have equal differences. A – B – C = A – C – B. The substitution postulate: If two quantities are equal, you may substitute one for the other in any expression. The partition postulate: any whole is equal to the sum of all of its parts. Line ABC = AB + BC.

CPCTC: corresponding parts of the congruent triangle are congruent SSS: side-side-side: if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent SAS: side-angle-side: if two triangles have a congruent side-angle-side, then the two triangles are congruent ASA: angle-side-angle: if two triangles have a congruent angle-side-angle, then the two triangles are congruent AAA: angle-angle-angle: triangles with congruent angles are similar, but not necessarily congruent