# Geometry chapter 3

## 53 terms

### Parallel Lines

coplanar lines that do not intersect

### Skew lines

non coplanar lines, therefore, they are neither parallel nor intersecting

do not intersect

### A line and a plane are parallel

if the do not intersect

### if two parallel planes are cut by a third plane

then the lines of intersection are parallel (T)

### transversal

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

### alternate interior angles

two nonadjacent interior angles on opposite sides of the transversal

### same side interior angles

two interior angles on the same side of the transversal

### corresponding angles

two angles in corresponding positions relative to the two lines

### if two parallel lines are cut by a transversal

then corresponding angles are congruent (P)

### if two parallel lines are cut by a transversal

then alternate interior angles are congruent (T)

### if two parallel lines are cut by a transversal

then same-side interior angles are supplementary (T)

### if a transversal is perpendicular to one of two parallel lines

then it is perpendicular to the other one also (T)

### if two parallel lines are cut by a transversal

then corresponding angles are congruent (P)

### if two lines are cut by a transversal and corresponding angles are congruent

then the lines are parallel (P)

### if two lines are cut by a transversal and alternate interior angles are congruent

the the lines are parallel (T)

### if two lines are cut by a transversal and same-side interior angles are supplementary

then the lines are parallel (T)

are parallel (T)

### through a point outside a line

there is exactly one line parallel to the given line (T)

### through a point outside a line

there is exactly one line perpendicular to the given line (T)

### two lines parallel to a third line

are parallel to each other (T)

### triangle

the figure formed by three segments joining three non collinear points

### scalene triangle

triangle with no sides congruent

### isosceles triangle

triangle with at least two sides congruent

### equilateral triangle

triangle with all sides congruent

### acute triangle

triangle with three acute angles

### obtuse triangle

triangle with one obtuse angle

### right triangle

triangle with one right angle

### equiangular triangle

triangle with all angles congruent

### auxiliary line

a line (or ray or segment) added to a diagram to help in a proof

is 180 (T)

### if two angles of one triangle are congruent to two angles of another triangle

then the third angles are congruent (C)

### each angle of an equiangular triangle

has measure 60 (C)

### in a triangle

there can be at most one right angle or obtuse angle (C)

### the acute angles of a right triangle

are complementary (C)

### the measure of an exterior angle of a triangle equals

the sum of the measures of the two remote interior angles (T)

three sides

four sides

five sides

six sides

eight sides

seven sides

nine sides

ten sides

twelve sides

n sides

### diagonal

the segment joining two nonconsecutive vertices

is (n-2)180 (T)

### convex polygon

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

### concave polygon

one or more vertex is interior

is 360 (T)

### regular polygon

if a polygon is both equiangular and equilateral

### inductive reasoning

a kind of reasoning that is widely used in science and in everyday life