Theorems
If two angles are equal to each other, then their supplements are equal to each other
Theorem 1
x = x
Reflexive Property
a + b = b + a
Symmetric Property
If A = B, and B = C, then A = C
Transitive Property of Equality
If the hypotenuse and one of the legs of one right triangle are equal to the hypotenuse and one of the legs of another right triangle, then the triangles are congruent
Hypotenuse Leg
Intersecting lines form opposite angles that are equal in pairs
Theorem 3
If a = b, then a + c = b + c
Addition Property of Equality
If a = b, then a - c = b - c
Subtraction Property of Equality
If A = B, then either may be substituted for the other in a statement of equality or inequality
Substitution
If all three sides of one triangle are equal to all three sides of another, then the two triangles are congruent
Side, Side, Side
If two sides of a triangle are equal, then the two angles opposite those sides are equal as well
Theorem 5
If a = b, then ac = bc
Multiplication Property of Equality
If a = b and c is not 0, then a/c = b/c
Division Property of Equality
If A > B, and B > C, then A > C
Transitive Property of Inequality
If two sides and the included angle of one triangle are equal to two sides and the included angle of another, then the triangles are congruent
Side, Angle, Side
If two angles are equal to each other, then their complements are equal
Theorem 2
If a > b, then a + c > b + c
Addition Property of Inequality
If a > b, then a - c > b - c
Subtraction Property of Inequality
The 14th president of the United States
If two angles and the included side of one triangle are equal to two angles and the included side of another, then the triangles are congruent
Angle, Side, Angle
If two angles of a triangle are equal, then the sides opposite those angles are equal as well
Theorem 6
If a > b and c>0, then ac > bc
Multiplication Property of Inequality
If a > b and c>0 , then a/c > b/c
Division Property of Inequality
What is the derivative of the following function:
f(x) = 3x
Angle, Angle, Side