# Chapter 3 Geometry

## 28 terms · Vocab, Theorems, and Postulates

### Parallel lines

are coplanar lines that do not intersect

### Skew lines

are non coplanar lines. There forth, they are are neither parallel nor intersecting.

### Theorem 3-1

If two parallel planes are cut by a third plane, then the lines of intersection are parallel

### Transversal

is a line that intersects two or more coplanar lines in different points.

### Alternate interior angles

are two nonadjacent interior angles on oposite sides of the transversal.

### Same-Side interior angles

are two interior angles on the same side of the transversal.

### Corresponding angles

are two angles in corresponding postions relative to the two lines

### Postulate 10

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

### Theorem 3-2

if two lines are cut by a transversal, then alternate interior angles are congruent.

### Theorem 3-3

If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

### Theorem 3-4

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.

### Postulate 11

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

### Theorem 3-5

If two lines are cut by a transversal and alternative interior angles are congruent, then the lines are parallel.

### Theorem 3-6

If two lines are cut by transversal same side interior angles are supplementary, then the lines are parallel

### Theorem 3-7

In a plane two lines are perpendicular to the same line are parallel.

### Theorem 3-8

Through a point outside a line, there is exactly one line parallel to the given line.

### Theorem 3-9

Through a point outside a line, there is exactly one line perpendicular to the given point.

### Theorem 3-10

Two lines parallel to a third line are parallel to each other

### Triangle

is a figure formed by three segments joining three non collinear points

### Theorem 3-11

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

### Corollary 1

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.

### Corollary 2

Each angle of an equiangular triangle has a measure 60

### Corollary 3

In a triangle, there can be at most one right angle

many angles

### Convex Polygon

a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.

### Diagonal

A segment joining two nonconsecutive vertices

### Theorem 3-13

The sum of the measure of the angles of a convex polygon with n sides is (n-2)180

### Theorem 3-14

The sum of the measures of the extrior angles of any convex polygon, one angle must be a vertex, is 360.