# Geometry Chapter 2 Postulates and Theorems

## 25 terms · Geometry Postulates and Theorems from the McGraw-Hill book.

### Through any two points, there is exactly.......?

Through any two points, there is exactly one line.

### Through any three non-collinear points, there........?

Through any three noncollinear points, there is exactly one plane

### A line contains at least.........?

A line contains at least two points

### A plane contains at least..................?

A plane contains at least three non-collinear points

### If two points lie in a plane, then the entire line containing those points..............?

If two points lie in a plane, then the entire line containing those points lies in that plane

### If two lines intersect, then their intersection is............?

If two lines intersect, then their intersection is exactly one point

### Ruler Postulate

The points on any line or line segment can be put into one-to-one correspondence with a real number; or a line have one point on zero and the other point on any real number greater than zero

If A, B, and C are collinear, then point B is between A and C if and only if AB+BC=AC

### Protractor Postulate

Given any angle, the measure can be put into one-to-one correspondence with real numbers between 0 to 180

∠D is the interior of angle ABC if and only if
m∠ABD + m∠DBC = m∠ABC

### Midpoint Theorem

if M is the midpoint of AB, then AM=MB, If M is the midpoint of segment AB, then segment AM is congruent to segment MB.

AB=AB

### Symmetry Property of Congruence

If AB=CD, then CD=AB

### Transitive property of Congruence

If AB ≅ CD and CD ≅ EF, then AB ≅ EF.

### Supplement theorem

if two angles form a linear pair, then they are supplementary angles.

### Complement Theorem

if the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

### Congruent Supplements Theorem

Angles Supplementary to the same or congruent angles are congruent

### Congruent Complements Theorem

Angles complementary to the same angle or to congruent angles are congruent

### Congruent Complements Theorem

Angles complementary to the same angle or to congruent angles are congruent

### Vertical Angles Theorem

Perpendicular angles form four right angles

### Perpendicular lines intersect to form.......?

Perpendicular lines intersect to form congruent adjacent angles

### All right angles are.......?

All right angles are congruent

### Perpendicular lines form.........?

Perpendicular lines form congruent adjacent angles

### If two angles are congruent and supplementary, then each..........?

If two angles are congruent and supplementary, then each angle is a right angle.

### If two congruent angles form a linear pair, then they are.......?

If two congruent angles form a linear pair, then they are right angles