# Theorems and Postulates

#### Study  only

Flashcards Flashcards

Scatter Scatter

Scatter Scatter

## Create a new folder

### If two angles are right angles, then

they are congruent

### If two angles are straight angles, then

they are congruent

### If a conditional statement is true, then

the contrapositive of the statement is also true (If p, then q <=> if ~q, then ~p.)

### If angles are supplementary to the same angle, then

they are congruent

### If angles are supplementary to congruent angles, then

they are congruent

### If angles are complementary to congruent angles, then

they are congruent

### If angles are complementary to congruent angles, then

they are congruent

### If a segment is added to two congruent segments, then

the sums are congruent. (Addition property)

### If an angle is added to two congruent angels, then

the sums are congruent. (Addition property)

### If congruent segments are added to congruent segments, then

the sums are congruent. (Addition property)

### if congruent angles are added to congruent angles, then

the sums are congruent. (Addition property)

### If a segment (or angle) is subtracted from congruent segments (or angles), then

the differences are congruent. (Subtraction Property)

### If congruent segments (or angles) are subtracted from congruent segments (or angles), then

the differences are congruent. (Subtraction Property)

### If segments (or angles) are congruent, then

their like multiples are congruent. (Multiplication Property)

### If segments (or angles) are congruent, then

their like divisions are congruent. (Division Property)

### If angles (or segments) are congruent to the same angle (or segment), then

they are congruent to each other. (Transitive Property)

### If angles (or segments) are congruent to congruent angles (or segments), then

they are congruent to each other. (Transitive Property)

congruent

congruent

### If two sides of a triangle are congruent, then

the angles opposite the sides are congruent.

### If two angles of a triangle are congruent, then

the sides opposite the sides are congruent.

### If A = (x1, y1) and B = (x2, y2), then

the midpoint M = (xm, ym) of AB can be found by using the midpoint formula

### If two angles are both supplementary and congruent, then

they are right angles

### If two points are each equidistant from the endpoints of a segment, then

the two points determine the perpendicular bisector of that segment

Example: