| A | B |
|---|
| Postulate 2-1 Through any two points, | ... there is exactly one line |
| Postulate 2-2 Through any three noncollinear points | ... there is exactly one plane containing them. |
| Postulate 2-3 If two points lie in a plane, | ... then the line containing those points lies in the plane. |
| Postulate 2-4 If two lines intersect, | ... then they intersect in exactly one point. |
| Postulate 2-5 If two planes intersect, | ... then they intersect in exactly one line. |
| Ruler Postulate | The points on a line can be put into a one to one correspondence with the real numbers. |
| Segment Addition Postulate (Seg. Add. Post) | If B is between A and C, then AB + BC = AC. |
| Protractor Postulate | Given line AB and a point O on line AB, all rays that can be drawn from O can be put into a one to one correspondence with the real numbers from 0 to 180. |
| Angle Addition Postulate (∠Add Post) | If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR. |
| Pythagorean Theorem | In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. |
| Linear Pair Theorem (Lin. Pair Thm) | If two angles form a linear pair, then they are supplementary. |
| Congruent Supplements Theorem (≅ Supp. Thm) | It two angles are supplementary to the same angle (or to two congruent angles), then the two angles are congruent. |
| Right Angle Congruence theorem (Rt. ∠ ≅Thm) | All right angles are congruent. |
| Congruent Complements theorem (≅Comps. Thm) | If two angles are complementary to the same angle (or two congruent angles), then the two angles are congruent. |
| Common Segments Theorem (Common Segs. Thm) | Given collinear points A, B, C and D arranged as shown, if segment AB ≅ segment CD then segment AC ≅ segment BD. |
| Vertical Angles Theorem (Vert ∡ Thm) | If two congruent angles are supplementary, then each angle is a right angle. Vertical angles are congruent. |
| Corresponding Angles Postulate (Corr ∡ Post) | If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. |
| Alternate Interior Angles Theorem (Alt. Int ∡ thm) | If two parallel lines are cut by a transversal, then the pairs of alternate interior angle are congruent. |
| Alternate Exterior Angles theorem (alt Ext. ∡ Thm) | If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent. |
| Same side interior angles theorem (Same-Side Int. ∡ Thm) | If two parallel lines are cut by a transversal then the two pairs of same side interior angles are supplementary |
| Converse of the Corresponding Angles Postulate (Conv. Of Corr. ∡ Post) | If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, the lines are parallel. |
| Parallel Postulate (Parallel Post) | Through a point P not on line l, there is exactly one line parallel to l. |
| Converse of the Alternate Interior Angles theorem. (Conv of Alt Int ∡ Thm) | If two coplanar lines are cut by a transversal so that a pair of alternate interior angle are congruent, then the two lines are parallel. |
| Converse of the Alternate Exterior Angles Theorem (Conv of Alt. Ext ∡ Thm) | If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel. |
| Converse of the Same-Side Interior Angles Theorem. (Conv. Of Same-Side Int. ∡ Thm) | If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines parallel. If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular |
| Perpendicular Transversal Theorem (⊥ Transv. Thm) | In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. |
| Parallel Lines Theorem (ll lines thm) | In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. |
| Perpendicular Lines Theorem (⊥ Lines Thm) | In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular. |
| Triangle Sum Theorem (△ sum thm) | The sum of the angle measures of a triangle is 180 degrees.The acute angles of a right triangle are complementaryThe measure of each angle of an equiangular triangle is 60 degrees.. |
| Exterior Angle Theorem. (Ext. ∠ Thm) | The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. |
| Third Angles theorem (Third ∡ Thm) | If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. |
| Side-Side-Side (SSS) Congruence Postulate | If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent (SSS) |
| Side-Angle-Side (SAS) Congruence Postulate | 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. |
| 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 another triangle, then the triangles are congruent. |
| Angle-Angle-Side (AAS) Congruence Theorem | If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent. |
| Hypotenuse-Leg (HL) Congruence Theorem | If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. |
| Isosceles Triangle Theorem (Isosc. △ Thm) | If two side of a triangle are congruent, then the angles opposite the sides are congruent. |
| Converse of the Isosceles Triangle Theorem (Conv. Of Isosc. △ thm) | If two angles of a triangle are congruent, then the sides opposite those angles are congruentIf a triangle is equilateral, then it is equiangular.. |
