Disjunction ORIn logic, a disjunction is a compound sentence formed by combining two sentences (or facts) using the word “or.” A disjunction is true when EITHER or BOTH sentences (or facts) are true.Examples: “Blue is a color or 7 + 3 = 10.” (T or T = T…

Conjunction ANDIn logic, a conjunction is a compound sentence formed by combining two sentences (or facts) using the word “and.” A conjunction is true only when BOTH sentences (or facts) are true.Examples: “Blue is a color and 7 + 3 = 10.” (T and T = T)…

Mean Proportional in a Right Triangle“Mean Proportional” may also be referred to as a “Geometric Mean”. Remember the rule for working with proportions: the product of the means equals the product of the extremes.Definition: The mean proportional of two …

Theorems and Postulates for GeometryThis is a partial listing of the more popular theorems, postulates and properties needed when working with Euclidean proofs. You need to have a thorough understanding of these items.General:Reflexive PropertyA quantit…

Simple Negation (NOT) StatementsIn logic, a negation of a simple statement (one logical value) can usually be formed by placing the word “not” into the original statement. The negation will always have the opposite truth value of the original statement. …

Tips for Working with Congruent Triangles in ProofsTwo triangles are congruent if all pairs of corresponding sides are congruent, and all pairs of corresponding angles are congruent. Fortunately, we do not need to show all six of these congruent parts ea…

Slopes and Equations of LinesLet’s review our knowledge of slopes and equations of lines.

Review of Transformations – Isometry StatusIsometry – length is preserved – the figures are congruent. Direct Isometry – orientation is preserved – the order of the lettering in the figure and the image are the same, either both clockwise or both counte…

Dilations and SimilaritySimilar figures are figures that are the same shape, but not necessarily the same size. If these figures should also be the same size, the figures are called congruent.In our study of transformations we have seen many figures tha…

Indirect Proof (Proof by Contradiction)When trying to prove a statement is true, it may be beneficial to ask yourself, “What if this statement was not true?” and examine what happens. This is the premise of the Indirect Proof or Proof by Contradiction.I…