math pt 2

• a statement is a sentence that can be judged as either true or false, but not both.
• The truth (T) or falsity (F) of a statement is the truth value.
• Two statements can be joined by AND or OR to form a compound statement.
• To form negation of a statement, insert the word NOT so that the original statement and its negation have opposite truth values.
• The negation of 𝑝 is denoted as ~𝑝 and is read as “not p.”
• A conjunction uses AND to connect two statements.
• Each of the statements that make up a conjunction is called a conjunct.
• A disjunction uses OR to connect two statements
• . Each of the statements that make up a disjunction is called a disjunct
• a disjunction is only true when at least one of the statements joined by the word or is true.
• A truth table summarizes the truth values a compound statement takes on for all possible combinations of truth values of the simple statements it compromises.
• Reflexive Property

  A quantity is congruent (equal) to itself. a = a
• Symmetric Property

  If a = b, then b = a
• Transitive Property

  If 𝑎 = 𝑏 and 𝑏 = 𝑐, then 𝑎 = c
• Addition Postulate

  If equal quantities are added to equal quantities, the sums are equal.
• Subtraction Postulate

  If quantities are subtracted from equal quantities, the differences are equal.
• Multiplication Postulate If equal quantities are multiplied by equal quantities, the products are equal. (Also doubles of equal quantities are equal.)
• Division Postulate If equal quantities are divided by equal nonzero quantities, the quotients are equal. (Also Halves of equal quantities are equal.)
• Substitution Postulate A quantity may be substituted for its equal in any expression.
• Partition Postulate

  The whole is equal to the sum of its parts. Also: Betweenness of points: 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶 Angle Addition Postulate: m∠𝐴𝐵𝐶 + m∠𝐶𝐵𝐷 = m∠𝐴𝐵D
• Right Angles

  All right angles are congruent
• Straight Angles

  All straight angles are congruent
• Congruent Compliments

  Complements of the same angle, or congruent angles, are congruent.
• Congruent Supplements

  Supplements of the same angle, or congruent angles, are congruent.
• Linear Pair

  If two angles form a linear pair, they are supplementary.
• Vertical Angles

  Vertical angles are congruent.
• Triangle Sum

  The sum of the interior angles of a triangle is 180°
• Exterior Angle

  The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. The measure of an exterior angle of a triangle is greater than nonadjacent interior angle.
• Base Angle Theorem (Isosceles Triangle)

  If two sides of a triangle are congruent, the angles opposite to these sides are congruent.
• Base Angle Converse

  If two angles of a triangle are congruent, the sides opposite to these angles are congruent.
• Side-Side-Side (SSS) Congruence

  If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent
• Side-Angle-Side (SAS) Congruence

  If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
• Angle-Side-Angle (ASA) Congruence

  If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
• Angle-Angle-Side (AAS) Congruence

  If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle the triangles are congruent.
• Hypotenuse-Leg (HL) Congruence (Right Triangle)

  If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.
• CPCTC

  Corresponding Parts of Congruent Triangles are Congruent
• Angle-Angle (AA) Similarity

  If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
• SSS for Similarity

  If three sets of corresponding sides of two triangles are in proportion, the triangles are similar.
• SAS for Similarity

  If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths o the sides including these angles are in proportion, the triangles are similar.
• Side Proportionality If two triangles are similar, the corresponding sides are in proportion.