| A | B |
|---|
| ReflexiveProperty | For every number a, a = a. |
| SymmetricProperty | For all numbers a & b, if a = b, then b = a.(ex. the segment GH = segment HG) |
| TransitiveProperty | For all numbers a, b & c, if a = b & b = c, then a = c. (A bit like the law of syllogism) |
| Add/Subtract Property | For all numbers a, b, & c, if a = b, then a + c = b + c and a - c = b - c.(ex. 1 ft = 12 inches, 1 ft + 3 inches = 12 in ches+ 3 inches) |
| Mult/Division Property | For all numbers a, b, and c, if a = b, then a * c = b * c, and if c not equal to zero, a ÷ c = b ÷ c.(ex. 1 m = 1000 mm, 1 m * 5 = 1000 mm * 5, 5 m = 5000 mm) |
| SubstitutionProperty | For all numbers a & b, if a = b, then a may be replaced by b in any equation or expression. |
| DistributiveProperty | For all numbers a, b, & c, a(b + c) = ab + ac. |
| THEOREM 2-1 Segment Properties | Congruence of segments is reflexive, symmetric, and transitive. |
| Theorem 2-2 Supplement Theorem | If two angles form a linear pair,then they are supplementary angles. |
| Theorem 2-3 Angle Properties | Congruence of angles is reflexive, symmetric, and transitive. |
| Theorem 2-4 supplementary congruent | Angles supplementary to the same angle or to congruent angles are congruent. |
| Theorem 2-5complementary congruent | Angles complementary to the same angle or to congruent angles are congruent. |
| Theorem 2-6 right congruent | All right angles are congruent. |
| Theorem 2-7 vertical angles | Vertical angles are congruent. |
| Theorem 2-8 perpendicular lines form | Perpendicular lines intersect to form four right angles.. |
| Postulate 3-1 Corresponding Angles | If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent., |
| Theorem 3-1 Alternate Interior | If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent, |
| Theorem 3-2 Consecutive Interior Angle | If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary |
| Theorem 3-3 Alternate Exterior Angle | If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent, |
| Theorem 3-4 Perpendicular Transversal | In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other., |
| Postulate 3-5 Euclidean Parallel Postulate | In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. |
| Theorem 3-5 transversal alt int angles | If there is a line and a point not on the line, then there exists exactly one line though the point that is parallel to the given line., |
| Theorem 3-5 transversal alt int angles | If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel., |
| Theorem 3-6 | If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel., |
| Theorem 3-8 | In a plane, if two lines are perpendicular to the same line, then they are parallel., |
| Theorem 3-7 | to be added |
| Postulate 3-2 | Two nonvertical lines have the same slope if and only if they are parallel., |
| Postulate 3-3 | Two nonvertical lines are perpendicular if and only if the product of their slopes is -1., |
| Postulate 3-4 | If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel., |
| Theorem 4-2 Third Angle Theorem | If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent., |
| Theorem 4-1 Angle Sum Theorem | The sum of the measures of the angles of a triangle is 180., |
| Theorem 4-3 Exterior Angle Theorem | The measure of an exterior angle of a trianlge is equal to, |
| Corollary 4-1 | The acute angles of a right triangle are complementary., |
| Postulate 4-1 SSS | (Side - Side - Side) - If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent., |
| Postulate 4-2 SAS | Side - Included Angle - Side) - If two sides and the INCLUDED angle of one triangle are congruent to two sides and the INCLUDED angle of another triangle, then the triangles are congruent., |
| Postulate 4-3 ASA | (Angle - Included Side - Angle) - If two angles and the INCLUDED side of one triangle are congruent to two angles and the INCLUDED side of another triangle, then the triangles are congruent. |
| Postulate 4-3 AAS | (Angle - Angle - Side) - If two angles and a NON-INCLUDED side of one triangle are congruent to the corresponding two angles and side of a second triangle, the two triangles are congruent. |
| Theorem 4-6 Isosceles Triangle Theorem (ITT) | If two sides of a triangle are congruent, then the angles opposite those sides are congruent., |
| Theorem 4-7 Converse of the ITT | If two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
| Corollary 4-3 | A triangle is equilateral if and only if it is equiangular. |
| Corollary 4-4 | Each angle of an equilateral triangle measures 60 degrees. |
| Theorem 5-5 LL (Leg - Leg) | If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent., |
| Theorem 5-6 HA (Hypotenuse - Angle) | If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent., |
| Theorem 5-7 LA (Leg - Angle) | If the leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent., |
| Postulate 5-1 HL (Hypotenuse -Leg) | If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. |
| Theorem 5-8 Exterior Angle Inequality Theorem | If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles., |
| Theorem 5-9 | If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite |
| Theorem 5-10 | If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle, |
| Theorem 5-11 | The perpendicular segment from a point to a line is the shortest segment from the point to the line., |
| Theorem 5-12 | The perpendicular segment from a point to a plane is the shortest segment from the point to the plane. |
| Theorem 5-12 Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
| Theorem 5-5 LL (Leg - Leg) | If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent., |
| Theorem 5-6 HA (Hypotenuse - Angle) | If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent., |
| Theorem 5-7 LA (Leg - Angle) | If the leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent., |
| Postulate 5-1 HL (Hypotenuse -Leg) | If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. |
| Theorem 5-8 Exterior Angle Inequality Theorem | If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles., |
| Theorem 5-9 | If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite |
| Theorem 5-10 | If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle, |
| Theorem 5-11 | The perpendicular segment from a point to a line is the shortest segment from the point to the line., |
| Theorem 5-12 | The perpendicular segment from a point to a plane is the shortest segment from the point to the plane. |
| Theorem 5-12 Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
| Theorem 5-2 | Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment |
| Theorem 5-3 | Any point on the bisector of an angle is equidistant from the sides of the angle |
| Theorem 5-4 | Any point on or in the interior of an angle and equidistant from the sides of an angle lies on the bisector of the angle |
