Right Angle Congruence Theorem
All right angles are congruent.
Congruent Supplements Theorem
If two angles are supplementary to the same angle, then they are congruent. If m<1 + m<3 = 180 and m<2 + m<3 = 180 then <1 is congruent to <3.
Congruent Complements Theorem
If two angles are complementary to the same angle, then they are congruent. If m<1 + m<3 = 90 and m<2 + m<3 = 90 then <1 is congruent to <3.
Linear Pair Postulate
If two angles form a linear pair, then they are supplementary (add up to 180 degrees).
Vertical Angles Theorem
Vertical angles are congruent.
Theorem 3.1
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Theorem 3.2
If two sides of two adjacent acute angles perpendicular, then the angles form 90 degrees by Angle Addition Postulate.
Theorem 3.3
If two lines are perpendicular, then they form FOUR 90 degree angles.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then their corresponding angles are congruent.
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then their alternate interior angles are congruent.
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the consecutive interior angles are SUPPLEMENTARY.
Alternate Exterior Angles Theorem
If two lines are parallel and are cut by a transversal, then their alternate exterior angles are congruent.
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other.
Corresponding Angles Converse Postulate
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Alternate Interior Angles Converse Theorem
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
Consecutive Interior Angles Converse Theorem
If two lines are cut by a transversal so that the consecutive interior angles add up to 180 degrees [supplementary], then the lines are parallel.
Alternate Exterior Angles Converse Theorem
If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel.
Theorem 3.11
If two lines are parallel to the same line, then they are parallel to each other.
Theorem 3.12
If two lines are perpendicular to the same line, then they are parallel to each other.
Slopes of Parallel Lines Postulate
Two lines that are parallel to each other have the same slope.
Slopes of Perpendicular Lines Postulate
If two lines are perpendicular, then the slope of one line is the negative reciprocal of the slope of the other line.
Triangle Sum Theorem
The sum of the interior angles of a triangle add up to 180 degrees.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is the sum of the measures of two nonadjacent interior angles.
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary [they add up to 90 degrees].
Third Angles Theorem
If two angles of a triangle are congruent to the two angles of another triangle, then the 3rd angles are also congruent to each other.
Reflexive Property of Congruent Triangles
Every triangle is congruent to itself.
Symmetric Property of Congruent Triangles
If triangle ABC = triangle DEF, then triangle DEF = triangle ABC.
Side-Side-Side Congruence Postulate
If three sides of a triangle are congruent to the corresponding three sides of another triangle, then the two triangles are equal.
Side-Angle-Side Congruence Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
Angle-Side-Angle 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.
Angle-Angle-Side Congruence Theorem
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite to them are congruent [the angles on the base].
Converse Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite to them are congruent [the legs].
Hypotenuse-Leg Congruence Theorem
If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.