# Math rules for geometry

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if a=b then a+c=b+c

### Subtraction property

if a=b then a-b=b-c

### Multiplication property

if a=b then a•c=b•c

### Division property

if a=b then a/b=b/c

a=a

if a=b then b=a

### transitive property

if a=b and b=c then a=c

### substitution property

if a=b then b can replace a in any expression

a(b+c)= ab+ac

### vertical angles

two angles whose sides form two pair of opposite rays

two coplanar angles with a common side, a common vertex, and NO common interior points

### complementary angles

two angles whose measures have a sum of 90

### supplementary

two angles whose measures have a sum of 180

### Vertical angle theorem

vertical angles are congruent

### Congruent supplements theorem

if two angles are supplements of the same angle (or of congruent angles) then the two angles are congruent

### Congruent complements theorem

if two angles are complements of the same angle (or of congruent angles) then the two angles are congruent
right angles are congruent
if two angles are congruent and supplementary then each is a right angle

### congruent angles

angles that have the same measure

### 2 points postulate

through any two points there is exactly one line

### 2 lines postulate

if two lines intersect then they intersect in exactly one point

### 2 planes postulate

if two planes intersect they intersect in exactly one line

### 3 points postulate

through any 3 noncollinear points there is exactly one plane

if three points A, B, C are collinear and B is between A and C the AB+BC=AC

if B is in the interior of <AOC then m<AOB+m<BOC=<AOC
if <AOC is a straight angle then <AOB+<BOC=180

less than 90

90

more than 90

180

### perpendicular lines

2 lines that intersect to form right angles

### angle bisector

a ray that divides an angle into two congruent coplanar angles

### Distance formula

√(x₂-x₁)²+(y₂-y₁)²

### Midpoint Formula

M= x₁+x₂/2, y₁+y₂/2

### transversal

a line that intersects to coplanar lines

### alternate interior angle

nonadjacent interior angles that lie on opposite sides of the transversal

### same side interior angles

lie on the same side of the transversal

### corresponding angles

lie on the same side of the transversal in corresponding positions

### Corresponding angles postulate

if a transversal intersects two parallel lines then corresponding angles are congruent

### alternate interior angles theorem

if a transversal intersects two parallel lines then alternate interior angles are congruent

### same side interior theorem

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

### converse of the corresponding angles postulate

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

### converse of the alternate interior angles theorem

if two lines and a transversal form alternate interior angles that are congruent then the two lines are parallel

### converse of the same side interior angles theorem

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

### parallel lines theorem

if two lines are parallel to the same line then they are parallel to each other

### perpendicular lines theorem

in a plane if two lines are perpendicular to the same line then they are parallel to each other

### Triangle angle sum theorem

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

### Triangle exterior angle theorem

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

### exterior angles of a polygon

angle formed by a side and an extension of an adjacent side

### remote interior angles

the 2 angles not near the exterior angle

### polygon

closed plane figure with at least three sides that are segments

### convex polygon

has no diagonal with points outside the polygon

### concave polygon

has at least one diagonal with points outside the polygon

### polygon angle sum theorem

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

### polygon exterior angle sum theorem

the sum of the measures of the exterior angles of a polygon one at each vertex is 360

### equilateral polygon

all sides are equal

### equiangular polygon

all angles are equal

### regular polygon

both angles and sides are equal

y=mx+b

Ax+By=C

y-y₁=m(x-x₁)

y₂-y₁
______

x₂-x₁

x=

y=

x=0

y=0

4 sides

5 sides

6 sides

7 sides

8 sides

9 sides

10 sides

11 sides

12 sides

### acute triangle

all of its angles are acute

### obtuse triangle

has one obtuse angle

### scalene triangle

no sides or angles congruent

### right triangle

has a right angle

### isosceles

at least 2 congruent angles

### slope of parallel lines

if two non vertical lines are parallel their slopes are equal.

### slopes of perpendicular lines

if two non vertical lines are perpendicular the product of their slopes is -1

Example:

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