| A | B |
|---|
| Postulate 1-2: SEGMENT ADDITION POSTULATE | ANSWER: If Q is between P and R, then PQ + QR = PR. If PQ + QR = PR, then Q is between P and R |
| Postulate 1-4: ANGLE ADDITION POSTULATE | ANSWER: If r is in the interior of <PQS, then m<PQR + m<RQS = m<PQS. If m<PQR + m<rQS = m<PQs, then R is in the interior of <PQS. |
| Postulate 2-1 TWO POINTS AND A LINE | ANSWER: Through any "two points" there is exactly "one line". |
| Postulate 2-2 THREE POINTS AND A PLANE | ANSWER: Through any "three points NOT on the same line" there is exactly "one plane". |
| Postulate 2-3: DEFINITION OF A LINE | ANSWER: A "line" contains at least "two points". |
| Potulate 2-4: POINTS AND PLANES | ANSWER: A "plane" contains at least "three points NOT on the same line". |
| Postulate 2-5: POINTS - LINES - AND PLANES | ANSWER: If "two points" lie in a "plane", then the "ENTIRE line" containing those two points "lies in that plane". |
| Postulate 2-6: INTERSECTING PLANES | ANSWER: If "two planes intersect", then their "intersection is a line". |
| Theorem 2-1: CONGRUENT SEGMENTS | ANSWER: "Congruence of segments" is reflexive, symmetric, and transitive. |
| Theorem 2-2: DEFINITION OF SUPPLEMENTARY ANGLES | ANSWER: If "two angles" form a "linear pair (a straight line)", then they are "supplementary angles". |
| Theorem 2-3: CONGRUENCE OF ANGLES | ANSWER: "Congruence of angles" is reflexive, symmetric, and transitive. |
| Theorem 2-4: CONGURENT SUPPLEMENTARY ANGLES | ANSWER: Angles supplementary to the "same angles or to congruent angles" are "congruent". |
| Theorem 2-5: CONGRUENT COMPLEMENTARY ANGLES | ANSWERS: Angles complementary to the "same angle or to congruent angles" are "congruents". |
| Theorem 2-6: RELATIONSHIP OF RIGHT ANGLES | ANSWER: All "right angles" are "congruent". |
| Theorem 2-7: RELATIONSHIP OF VERTICAL ANGLES | ANSWER: "Vertical angles" are "congruent". |
| Tehorem 2-8: ANGLES FORMED BY PERPENDICULAR LINES | ANSWER: "Perpendicular lines" intersect to form "four (4) right angles". |
| Postulate 3-1: CORRESPONDING ANGLES' POSTULATE | ANSWER: If "two (2) parallel lines" are "cut by a transversal", then "each pair of corresponding angles" are "congruent". |
| Theorem 3-1: ALTERNATE INTERIOR ANGLE THEOREM | ANSWER: If "two (2) parallel lines" are "cut by a transversal", then "each pair of alternate interior angles" are congruent. |
| Theorem 3-2: CONSECUTIVE INTERIOR ANGLE THEOREM | ANSWER: If "two (2) parallel lines" are "cut by a transversal", then "each pair of consecutive interior angles" are "supplementary". |
| Theorem 3-3: ALTERNATE EXTERIOR ANGLE THEOREM | ANSWER: If "two (2) parallel lines" are "cut by a transversal", then "each pair of alternate exterior angles" are "congruent". |
| Theorem 3-4: PERPENDICULAR TRANSVERSAL THEOREM | ANSWER: In a "plane", if "a line is perpendicular to one of two (2) parallel lines", then "it is perpendicular to the other". |
| Postulate 3-2: CONGRUENT CORRESPONDING ANGLES AND PARALLEL LINES | ANSWER: If "two (2) lines" are "cut by a transversal" so that "corresponding angles" are "congruent", then "the lines are parallel. |
| Postulate 3-3: PARALLEL LINE AND A POINT POSTULATE | ANSWER: If there is "a line and a point NOT on the line", then "there exists exactly ONE line through the point" that "is parallel to the given line". |
| Theorem 3-5: CONGRUENT ALTERNATE INTERIOR ANGELS AND PARALLEL LINES | ANSWER: If "two (2) lines" are "cut by a transversal" so that"a pair of alternate interior angles" are "congruent", then "the two (2) lines are parallel." |
| Theorem 3-6: CONSECUTIVE INTERIOR ANGLES AND PARALLEL LINES | ANSWER: If "two (2) lines" are "cut by a transversal" so that "a pair of consecutive interior angles is supplementary", then "the lines are parallel". |
| Thorem 3-7: CONGRUENT ALTERNATE ANGLES AND PARALLEL LINES | ANSWER: If "two (2) lines" are "cut by a transversal", then the "lines are parallel". |
| Theorm 3-8: PERPENDICULAR LINES AND PARALLEL LINES | ANSWERS: In "a plane", if "two (2) lines" are "perpendicular to the SAME line", then "they are parallel". |
| Postulate 3-4" SLOPE AND PARALLEL LINES | ANSWERS: "Two (2) lines" have "the SAME slope" if and ONLY if "they are parallel and nonvertical".. |
| Postulate 3-5: SLOPE AND NONVERTICAL LINES | ANSWER: "Two (2) nonvertical lines" are "perpendicular" if and ONLY if "the PRODUCT of their slopes is - 1". |
| Theorem 4-1: ANGLE SUM THEOREM | ANSWER: The "SUM of the measures of the angles of a triangle" is "180 degrees". |
| Theorem 4-2: THIRD ANGLE THEOREM | ANSWER: If "two (2) angles of one trainagle" are "congruent to two (2) angles of a second triangle", then "the THIRD angles of the triangles are congruent". |
| Theorem 4-3: EXTERIOR ANGLES THEOREM | ANSWER: The "measures of an exterior angle of a triangle" is "EQUAL to the SUM of the measures" of the "two (2) REMOTE interior angles". |
| Corollary 4-1: ACUTE ANGLES AND RIGHT TRIANGLES | ANSWER: The "acute angles" of a "right triangle" are "complementary". |
| Collorary 4-2: RIGHT OR OBTUSE ANGLES AND TRIANGLES | ANSWER: There can be at most "ONE right or obtuse angle in a triangle". |
| Theorem 4-4: CONGRUENCE OF TRIANGLES | ANSWER: "Congruence of triangles" is "reflexive, symmetric, and transitive". |
| Postulate 4-1: SIDE - SIDE - SIDE (SSS) POSTULATE | ANSWER: If "the sides of one triangle" are "congruent to the sides of a SECOND triangle", then the "triangles are congruent". |
| Postulate 4-2: SIDE - ANGLE - SIDE (SAS) POSTULATE | ANSWER: If "two (2) sides and the INCLUDED angle of one triangle" are "congruent" to two (2) sides and an INCLUDED angles of ANOTHER triangle", then "the triangles are congruent. |
| Postulate 4-3: ANGLE - SIDE - ANGLE (ASA) POSTULATE | ANSWER: If "two (2) angles and the INCLUDED side of one triangle" are "congruent" to two (2) angles and the INCLUDED side of ANOTHER triangle, then the triangles are congruent". |
| Theorem 4-5: ANGLE - ANGLE - SIDE (AAS) THEOREM | ANSWER: If "two (2) angles and an NON-INCLUDED side of one triangle" are "congruent" to the corresponding two (2) angles and side of a SECOND triangle, the two (2) triangles are congruent". |
| Theorem 4-6: ISOCELES TRIANGLE THEOREM | ANSWER: If "two (2) sides of a triangle" are "congruent", the "angles OPPOSITE those sides are congruent". |
| Corollary 4-3: EQUILATERAL AND EQUIANGULAR TRANGLES | ANSWER: "A triangle is EQUILATERAL (ALL THREE SIDES BEING EQUAL)" if AND only if "it is EQUIANGULAR (all three angles are equal)" |
| Corollary 4-4: EQUILATERAL TRIANGLES AND ANGULAR MEASUREMENTS | ANSWERS: "Each ANGLE" of "a equilateral triangle measures 60 degrees". |
| Theorem 4-7: CONGRUENT ANGLES AND OPPOSITE SIDES | ANSWER: It "two (2) angles of a triangle" are "congruent", then "the side OPPOSITE those angles are congruent". |
