# Ch. 3 Definitions, Postulates, and Theorems to be used in Proofs

## 56 terms

### congruent (≅)

Vertical angles are

Right angles are

### Any time you change from = to ≅

When do you use definition of congruent angles?

### If (ray)BD bisects ∠ABC, then ∠ABD≅∠DBC

Definition of angle bisector

Transitive POC

Reflexive POC

Symmetric POC

### Supplements of the same angle are congruent Supplements of congruent angles are congruent

Supplementary angles

### Complements of the same angle are congruent Complements of congruent angles are congruent

Complementary angles

Perpendicular (⊥) lines form

### If M is the midpoint of (segment)AB, (segment)AM≅(segment)MB

Definition of midpoint

### Definition of midpoint

If M is the midpoint of (segment)AB, (segment)AM≅(segment)MB

### ...

Definition of segment bisector

### If (seg.)AB≅(seg.)CD and (seg.)CD≅(seg.)XY, then (seg.)AB≅XY

Transitive property

### Transitive Property

If (seg.)AB≅(seg.)CD and (seg.)CD≅(seg.)XY, then (seg.)AB≅XY

### Reflexive property

(seg.)JK≅(seg.)JK

### Angles which form linear pairs are supplementary

Linear pair postulate

### Linear pair postulate

Angles which form linear pairs are supplementary

### The sum of measures equals 180

Definition of supplementary angles

### Definition of supplementary

The sum of measures equals 180

### The sum of measures = 90

Definition of complementary angles

### Corresponding angles are ≅; Alternate interior angles are ≅; Alternate exterior angles are ≅

If two parallel lines are transversal, then

### corresponding angles are ≅

If lines are parallel, then

### the third angle is also ≅ (Third Angles Corollary)

If two angles of one triangle are congruent to two angles of another,

### ...

Definition of isosceles

### ...

Definition of equilateral

### angles are complementary

If exterior sides of adjacent angles are perpendicular,

### complementary

Acute angles of a right triangle are

### supplementary

If lines are parallel, then same-side interior angles are

### Lines that intersect in a right angle

Definition of perpendicular

### If measures = 90

Definition of right angle

### 4 right angles

Perpendicular lines from

### they are perpendicular

If 2 lines form congruent adjacent angles,

### then it is perpendicular to the other one

If a transversal is perpendicular to one of two parallel lines,

### Coplanar lines that do not intersect

Definition of parallel lines

### Definition of parallel lines

Coplanar lines that do not intersect

### lines are parallel

If corresponding angles are congruent, then

### lines are parallel

If alternate interior angles are congruent, then

### lines are parallel

If alternate exterior angles are congruent, then

### lines are parallel

If same-side interior angles are supplementary, then

### parallel

In a plane, 2 lines perpendicular to the same line are

### parallel to each other

2 lines parallel to the same line are

### Substitution

Is the equation similar to one in an earlier step?

### Addition POE; subtraction POE; multiplication POE; division POE

Did they do the same thing to both sides of an earlier step?

### ab+cb=(a+c)b (used to add like terms)

Distributive Property

### 180

Sum of angles in a triangle =

### 60

Each angle of an equilateral triangle =

### sum of remote interior angles

Measure of the exterior angles of a triangle =

m∠1+m∠2=m∠ABC

AB+BC=AC

ab+cb=(a+c)b

### Symmetric POC

If ∠1≅∠2, then ∠2≅∠1

∠A≅∠A

### Transitive POC

If ∠1≅∠2 and ∠2≅∠3, then ∠1≅∠3