Postulates
Theorems
Definitions

Postulates

1-5 | 6-10 | 11-15 | 16-20

  1. Ruler Postulate
     The points on a line can be matched, one-to-one, with the set of real numbers. The real number that corresponds to a point is the coordinate of the point. The distance, AB, between two points, A and B, on a line is equal to the absolute value of the difference between the coordinates of A and B. (page 64)

  2. Segment Addition Postulate
     If B is between A and C, then AB + BC = AC. (page 64)

  3. Protractor Addition Postulate
     Let ray OA be a ray and consider one of the half-planes P determined by the line OA. The rays of the form ray OD, where D is in a half-plane P, can be put in one-to-one correspondence with the real numbers between 0 and 180, including 180. If C and D are in the half-plane P, then the measure of angle COD is equal to the absolute value of the difference between the real numbers for ray OC and ray OD. (page 65)

  4. Angle Addition Postulate
     If B is in the interior of angle AOC, then the measure of AOB + the measure of BOC = the measure of AOC. (page 65)

  5. Linear Pair Postulate
     If two angles form a linear pair, then they are supplementary; that is, the sum of their measures is 180 degrees. (page 90)

  6. Parallel Postulate
     If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. (page 113)

  7. Perpendicular Postulate
     If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. (page 113)

  8. Corresponding Angles Postulate
     If two parallel lines are cut by transversal, then the pairs of corresponding angles are congruent. (page 135)

  9. Corresponding Angle Converse
     If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. (page 141)

  10. Side-Side-Side (SSS) Congruence Postulate
     If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. (page 177)

  11. Side-Angle-Side (SAS) Congruence Postulate
     If two sides and the included angle of one triangles are congruent to two sides and the included angle of a second trianges, then the two triangles are congruent. (page 178)

  12. Angle-Side-Angle (ASA) Congruence Postulate
     If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. (page 183)

  13. Angle-Angle (AA) Simliarity Postulate
     If two angles of one triangles are congruent to two angles of another triangle, then the two triangles are similar. (page 394)

  14. Arc Addition Postulate
     The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. (page 493)

  15. Area of a Square Postulate
     The area of a square is the square of the lengh of its side, or A = s2. (page 534)

  16. Area Congruence Postulate
     If two polygons are congruent, then they have the same area. (page 534)

  17. Area Addition Postulate
     The area of a region is the sum of the areas of all its nonoverlapping parts. (page 534)

  18. Volume of a Cube Postulate
     The volume of a cube is the cube of the length of its side, or V = s3. (page 607)

  19. Volume Congruence Postulate
     If two polyhedrons are congruent, then they have the same volume. (page 607)

  20. Volume Addition Postulate
     The volume of a solid is the sum of the volumes of all its nonoverlapping parts. (page 607)

Theorems

1-5 | 6-10 | 11-15 | 16-20 |

    2.1 Congruent Supplements Theorem
     If two angles are supplementary to the same angle or to congruent angles, then they are congruent. (page 91)

    Congruent Complements Theorem
     If two angles are complementary to the same angle or to congruent angles, then they are congruent. (page 91)

    Vertical Angles Theorem
     If two angles are vertical angles, then they are congruent. (page 92)

    Transitive Property of Parallel Lines
     If two lines are parallel to the same line, then they are parallel to each other. (page 105)

    Property of Perpendicular Lines
     If two coplanar lines are perpendicular to the same line, then they are parallel to each other. (page 106)

    Alternate Interior Angles Theorem
     If two parallel lines are cut by a transvesal, then the pairs of alternate interior angles are congruent. (page 135)

    Consecutive Interior Angles Theorem
     If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. (page 135)

    Alternate Exterior Angles Theorem
     If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. (page 135)

    Perpendicular Tranversal Theorem
     If a tranversal is perpendicular to one of two paralell lines, then it is perpendicular to the second. (page 135)

    Alternate Interior Angles Converse
     If Two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. (page 141)

    Consecutive Interior Angles Converse
     If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel. (page 141)

    Alternate Exterior Angles Converse
     If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. (page 141)

    Definitions

    A-E | F-J | K-T | U-Z |

  1. Acute Angle
     An acute angle is an angle with measure greater than 0 degrees and less than 90 degrees.

  2. Acute Triangle
     An acute triangle has three acute angles.

  3. Adjacent Angles
     Two angles are adjacent if they share a common vertex and side, but have no common interior points.

  4. Angle
     An angles consists of two different rays that have the same initioal point. The rays are the sides of the angle and the initial point is the vertex of the angle.

  5. Angle Bisector
     A ray that divides the angle into two congruent angles.

    B

  6. Biconditional Statement
     "p if and only if q," is written as p<-->q. This single statement is equivalent to writing the conditional statement p--> and its convers q-->.

    C

  7. Collinear
     Points, segments, or rays that are on the same line.

  8. Complementary Angles
     Two angles with the sum of their measures equalling 90 degrees. Each angle is a complement of each other.

  9. Congruent Angles
     Two angles are congruent if they have the same seasure.

  10. Contrapositive
     A conditional statement p-->q is ~q-->~p. The contrapositive of a conditional statement is true if and only if the conditional statement is true.

  11. Converse
     A conditional statement is formed by interchanging the hypothesis and conclusion. The converse of p-->q is q-->p.