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Theorems, postulates and definitions

### Midpoint

If a point is the midpoint of a segment, then it divides rhe segment into two congruent parts.

### Complements of the same angle are congruent

If two angles are each complementary to a third angle, then they're congruent to each other.

### Complements of congruent angles are congruent

If two angles are complementary to two other congruent angles, then they're congruent.

### Supplements of the same angle are congruent

If two angles are supplementary to the same angle, then they're congruent.

### Supplements of congruent angles are congruent

If two angles are supplementary to two other congruent angles, then they're congruent to each other.

### segment addition (three total segments)

if a segment is added to two congruent segments, then the sums are congruent.

### angle addition (three total angles)

if an angle is added to two congruent angles, then the sums are congruent.

### segment addition (four total segments)

if two congruent angles are added to two other congruent angles, then the sums are congruent.

### angle addition (four total angles)

if two congruent angles are added to two other congruent angles, then the sums are congruent

### segment subtraction (three total segments)

if a segment is subtracted from two congruent segments, then the differences are congruent.

### angle subtraction (three total segments)

if an angle is subtracted from two congruent angles, then the differences are congruent.

### segment subtraction (four total segments)

if two congruent segments are subtracted from two other congruent segments, then the diferences are congruent.

### angle subtraction (four total angles)

if two congruent angles are subtracted from two other congruent angles, then the differences are equal.

### transitive property (for three segments or angles)

if two segments (or angles) are congruent to a third segment or angle, then they're congruent to each other.

### transitive property (for four segments or angles)

if two segments or angles are congruent to congruent segments or angles, the they're congruent to each other.

### substitution property

if two geometric objects are congruent, then you can substitute one for the other.

### SSS

(side-side-side) if three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.