honors geo sem 1

Point

represented by a dot; no dimensions

Line

Represented by a line with 2 arrowheads but extends without end; 1 dimension

Plane

Represented by a shape that looks like a floor/wall but extends without end; 2 dimensions

collinear points

points that lie on the same line

coplanar points

points that lie on the same plane

Ray

e.g. the ray AB consists of the endpoint A and direction of B. First letter tells endpoint, second letter tells direction ALWAYS.

Opposite rays

If point C lies on AB between A and B, then CA and CB are opposite rays.

Postulate

a statement that is accepted as true without proof

Theorem

a statement that can be proven

Ruler postulate

The points on a line can be matched one to one with the real numbers

Def. congruent segments

If AB\=CD then AB is congruent to CD

Segment Addition Postulate

If B is between A and C, then AB + BC \= AC

Def. midpoint

A point that divides a segment into two congruent segments.

Def. segment bisector

any segment, line, or plane that intersects a segment at its midpoint. THIS DOES NOT STATE ANYTHING ABOUT CONGRUENCE.

Midpoint formula

Distance formula

Def. polygon

A closed plane figure formed by 3 or more line segments called sides. pretty self-explanatory ngl.

vertex

each endpoint of a side.

convex/concave

Convex: when no line that contains a side of the polygon contains a point in the interior of the polygon

Concave: not convex :)

NAME SOME POLYGONS

triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, and dodecagon. boom.

Perimeter (aka the thing you've known since like 4th grade)

the length around a figure

area (also something you've known since 4th grade)

the amount of surface covered by a figure

triangle perimeter/area

P\= a+b+c

A\= 1/2bh

square perimeter/area

P \= 4s

A \= s^2

Rectangle perimeter/area

P \= 2l + 2w

A \= lw

\____ ft \= \___ yd

3 ft \= 1 yd

\___ in \= \___ ft

12 in \= 1 ft

\_____ ft \= 1 mile

5280 ft \= 1 mile. DONT FORGET THIS I FAILED A TEST BC I MESSED THIS UP

def. acute angle

0° < x < 90°

def. right angle

x \= 90°

def. obtuse angle

90° < x < 180°

def. straight angle

180°

def. congruent angles

Two angles are congruent if and only if their measures are equal.

angle addition postulate

If P is in the interior of

def. angle bisector

a ray that divides an angle into two congruent angles

def. complementary angles

two angles whose measures have a sum of 90

def. supplementary angles

two angles whose measures have a sum of 180

def. adjacent angles

two angles that share a common vertex and side, but have no common interior points

def. linear pair

a pair of adjacent angles whose non-common sides are opposite rays

def. vertical angles

two angles whose sides form two pairs of opposite rays

TAKE A BREAK

GO DRINK SOME WATER OR STRETCH

conditional statement

a logical statement that has 2 parts, a hypothesis and a conclusion

"instance" of a conditional

an example that makes the statement true

"counterexample" of a conditional

an example that makes the statement false. you only need one of these to make the conditional false.

if-then form

conditional statement where "if" is the hypothesis & "then" is the conclusion.

Antecedent (hypothesis)

The clause following the word "if" in an if-then statement

Consequent (conclusion)

The clause following the word "then" in an if-then statement.

negation

pretty straight forward; denoted by ~p (not p)

converse

THE SHOE

jk u just switch the hypothesis and conclusion

Inverse

negating both the hypothesis and conclusion of the conditional

contrapositive

the negation of the converse

What are the equivalent statements??

conditional and contrapositive; converse and inverse

def. perpendicular lines

If two lines intersect to form a right angle, then they are perpendicular lines.

biconditional

"if and only if"

truth tables but simplified

conditional and contrapositive have the same concluding column of "true F**K true true". converse and inverse have the same concluding column of "true true F**k true" :)

Conjecture

an unproven statement that is based on observations

Inductive reasoning

stereotyping; finding patterns

deductive reasoning

using facts, definitions, accepted properties, and the laws of logic to form a logical argument

Law of Detachment

if the hypothesis of a true conditional statement is true, then the conclusion is also true

Law of Syllogism

If p--\>q and q--\>r are true statements, then p--\>r is a true statement.

Two Point Postulate

Through any two points there exists exactly one line

Line-Point Postulate

A line contains at least two points

Line Intersection Postulate

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

Three Point Postulate

Through any three noncollinear points there exists exactly one plane

Plane-Point Postulate

A plane contains at least 3 noncollinear points

Plane-Line Postulate

If two points lie in a plane, then the line containing them lies in the plane

Plane Intersection Postulate

If two planes intersect, then their intersection is a line.

Def. Line Perpendicular to a plane

a line and a plane are perpendicular iff they intersect and the line is perpendicular to all lines in the plane that pass through the point of intersection.

Addition Property of Equality

If a\=b, then a+c\=b+c

Subtraction Property of Equality

If a\=b, then a-c\=b-c

Multiplication Property of Equality

If a\=b, then ac\=bc

Division Property of Equality

if a \= b and c is not equal to 0, then a/c \= b/c

Substitution Property of Equality

If a\=b, then b can be substituted for a in any expression

Reflexive Property

a \= a

Symmetric Property

If a \= b, then b \= a

Transitive Property

If a\=b and b\=c, then a\=c

Right angles congruence theorem

All right angles are congruent

Congruent Supplements Theorem

If two angles are supplementary to the same angle, then they are congruent

Congruent Complements Theorem

if two angles are complementary to the same angle, then they are congruent

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary

Vertical Angles Congruence Theorem

Vertical angles are congruent

parallel lines

coplanar lines that do not intersect

skew lines

non-coplanar lines that do not intersect. think of a line on a ceiling and floor.

Parallel planes

two planes that do not intersect. think of ceiling and floor.

Parallel postulate

Through a point not on a line, there is one and only one line parallel to the given line.

Perpendicular Postulate

If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Transversal

a line that intersects two or more lines

Def. corresponding angles

Angles lie on the same side of the transversal and in corresponding positions.

Def. alternate interior angles

Two angles lie between the two lines and on opposite sides of the transversal

Def. alternate exterior angles

Two angles lie outside the two lines and on opposite sides of the transversal

Def. consecutive interior angles

Two angles lie between the two lines and on the same side of the transversal.

Corresponding angles theorem

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

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.