# Chapter 3 Geometry Postualtes/Theorems

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Postulates and theorems in chapter 3

### Postualte 3.1- Corresponding Angles Postulate

If a transversal intersects two lines, then corresponding angles are congruent

### Theorem 3.1- Alternate Interior Angles Theorem

If a transversal intersects two lines, then alternate interior angles are congruent

### Theorem 3.- Same-Side interior Angles theorem

If a transversal intersects two parallel lines, then the same side interior angles are supplementary

### Theorem 3.3- Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then alternate exterior angels are congruent

### Theorem 3.4- same side exterior angles theorem

if a transversal intercets two parallel lines, then same side exterior angles are supplementary.

### Postulate 3.2- Converse of corresponding angles postulate

If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel

### theorem 3.5- Converse of Alternate interior angles theorem

If two lines and a trnsversal form alternate interior angels that are congruent, then the two lines are parallel

### Theorem 3.6- Converse of same side interior angles theorem

If two lines and a transversal form same side interior angles that are supplementary, then the two lines are parallel

### Theorem 3.7- Converse of Alternate exterior angles theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel

### Theorem 3.8- Converse of same side exterior angles theorem

If two lines and a transversal form same side exterior angles that are supplementary, then the two lines are parallel

### Theorem 3.9

If two lines are paralle to the same line, then they are parallel to eachother

### Theorem 3.10

In a plane, if two lines are perpendicular to the same line then thay are paraller to each other

### Theorem 3.11

In a plane,is a line is perpenduiclar to one of two parallel lines, then it is also perpenduicular to the other

### Theroem 3.12- Triangle ANgle sum theorem

The sum of the measure of the angles of a triangle is 180

### Theorem 3.13- triangle exterior angle theorem

The measure of each exterior angle of a triangle equals the sum of the measure of its two remote interior angles

### Theorem 3.14- Polygon angle sum theorem

The sum of the measure of the angles of an n-gon is (n-2)180

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