Geometry

Interior formula

(n-2) * 180 I = -------------- 2

The sum of all three angles in a triangle equal ?

180 degrees

Exterior formula

360 E = -------- n

The acute angle of a right triangle are ?

Complementary (The sum of two angles equal 90 degrees)

If two lines are parallel to a third line then these lines are

Parallel to each other

collinear

point on the same line

Strategy for indirect proof

1. Assume temporarily that (the opposite of the prove statement) 2. Then.....try to get a statement that contradict the given 3. But this contradict the given fact that (given) 4. Therefore, the temporarily assumption that......#3......is false 5. It follows that (the prove statement "GIVEN")............

Write the indirect proof GIVEN - AB > BC PROVE - B is not the midpoint of SEGMENT AC

1. Assume temporarily that B is the midpoint of segment AC 2. Then AB is not > BC 3. But this contradict the given fact that AB is > BC 4. Therefore, the temporarily assumption that B is midpoint of segment AC is false 5. It follows that B is not the midpoint of AC

How to construct congruent angle

1. Put needle on vertex n draw circle 2. Put needle on outside of circle but extend bigger than vertex, do this both side to get line

Properties of congruent triangles

1. Reflexives property of congruence: /\ABC congruent to /\ABC 2. Symmetric property of congruence: /\ABC congruent to /\DEF, then /\DEF congruent to /\ABC 3. Transitive property of congruence: if /\ABC congruent to /\DEF and /\DEF congruent to /\GHI then /\ABC is congruent to /\GHI

Five ways of proving congruent triangles

1. SSS (side side side - if 3 side of one triangle are congruent to the 3 side of second triangle, then the triangle are congruent ) 2. SAS (side angle side - if two sides and the included angle of one triangle are congruent to two side and the included angle of a second triangle the the triangle are congruent) 3. ASA (angle side angle - if two angle and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the second triangle is congruent ) 4. AAS ( angle angle side - if two angles and a non-included side of a triangle are congruent to two angles and a non-included sides of a second triangle, then the triangles are congruent) 5. HL (Hypotenuse-Leg - when a leg and a hypotenuse of one triangle are congruent to a leg and a hypotenuse of another right triangle then the triangle are congruent)

Name, in order, the five parts of the formal proof of a theorem.

1. statement 2. drawing 3. given 4. prove 5. proof

Each angle of an equiangular triangles measures ?

60 degrees

Polygon

A closed plane figure whose sides are lines segments that intersect only at the endpoints

Paralellogram

A quadrilateral in which both opposite sides are parallel

Triangles classified by angles

Acute - all angles acute measure between 0 and 90 degrees Obtuse - one obtuse angle measure more than 90 degrees Right - one right angle Equiangular - all angles congruent

give the meaning of CD, CD ^ ----, CD, and CD ^-->

CD^ means line CD CD^ --- means line segment CD CD means the measure or Length of CD^ ---

Indirect proof

Conditional (or implication) - if P then Q Converse of conditional - if Q then P Inverse of condition - if not P then Q Contrapositive of condition - if not Q then not P

If two angles of a triangle are congruent to two angles of another triangle then the third angles are also !

Congruent

If two lines are cut by a transversal then the alternate interior angles are ?

Congruent

If two parallel line are cut a transversal then the alternate exterior angles are ?

Congruent

Two angle are ? If one coincides (fit perfectly over) the other

Congruent

CPCTC

Corresponding parts of congruent triangles are congruent

Transitive property

It keep going..if A=B and B=C and C=D that mean A=D so the first one always equal the last and so does everything in between.

Reflexive property

Mirror or reflection...when A is congruent to itself

If two lines are cut by a transversal so that the alternate exterior angles are congruent then these line are

Parallel

If two lines are cut by a transversal so that the corresponding angles are congruent then these lines are

Parallel

If two lines are cut by a transversal so that the exterior angle on the same side of the transversal are supplementary then these line are

Parallel

If two lines are cut by a transversal so that the same side interior angles are supplementary, then these line are

Parallel

If two coplanar lines are each perpendicular to a third lines, then these lines are

Parallel to each other

A concave polygon have at least one ?

Reflex angle

Sum of the measures

S = (n-2) * 180

Triangles classified by congruent sides

Scalene - none Isosceles - two sides Equilateral - 3 sides

If two parallel lines are cut by a transversal then the interior angles on the same side of the transversal are

Supplementary (the sum of measure of two angles equal 180 degrees)

Symmetric property

Symmetry, same on both side, its symmetrical

Convex polygon

The angles measure are between 0 and 90 degrees

A diagonal of a polygon is a line segment that join ?

Two nonconsecutive vertices

lines

a line is an infinite set of points

transversal

a line that intersect 2 or more lines at distinct points

segment

a segment is a line that could contain line segment as part of it *a straight line*

statement

a set of words and symbols that collectively make a claim that can be classified as true or false

postulate

a statement that is assumed to be true

intuition (based on how you feel)

a sudden insight allows one to make a statement without applying any formal reasoning

bisected angle

an angle divided into 2 congruent angles

obtuse angle

an angle that measure between 90 and 180 degrees

corresponding angles

angles that that lie in the same relative positions (above the parallel line and left of the transversal)

adjacent angles

angles who have a common vertex and a common side between them

if two line intersect, they intersect where?

at a point

circle

collection of point that are equal distance from the center

bisect

cut in half

alternate exterior

exterior (ext.) angles that lie on opposite sides of the transversal

same side exterior angles

exterior angles that lie on the same side of t transversal

conditional (or implication) converse of conditional inverse of conditional contrapositive of conditional

if P then Q if Q, then P if not P, then not Q if not Q, then not P

alternate interior

interior (int.) angle'\s that lie on opposite sides of the transversal

same side interior

interior angles that lie on the same side of the transversal

disjunction

is false only when P and Q are both false ( 4 + 3 = 7 or Cypress College is in the city of Fullerton )

conjunction

is true only when P and Q are both true ( 4 + 3 = 7 and Cypress College is in the city of Cypress )

parallel line

lines that lie in the same plane but do not intersect

straight angle

measure 180 degrees **double right angle**

acute angle

measure between 0 and 90 degrees

right angle

measure exactly 90 degrees

reflex angle

measures more than 180 degrees

Total number of diagonals

n(n-3) D = --------- 2

skew

neither parallel nor at right angles to a specified or implied line; askew; crooked.

the measure or length of a line segment is a

number

perpendicular lines

perpendicular line form to make 2 congruent adjacent angles

point

point are represented by a dot labeled with a single capital letter

midpoint

point in the middle

non coplanar points

points not on the same plane

coplanar points

points on the same plane

Does the relation "is greater than" have a reflexive property (consider real number A)? a symmetric property (consider real numbers A and B)? a transitive property (consider real numbers A, B, and C)?

reflexive # cannot be greater than itself. symmetric # cannot be greater than or less than itself. Only transitive # work because #A can be greater than #B and #B is greater than #C.

Does the relation "is less than" for numbers have a reflexive property (consider one number)? a symmetric property (consider two numbers)? a transitive property (consider three numbers)?

reflexive # cannot be less than itself. symmetric # cannot be less or greater than itself. Only transitive # will work because #A can be less than #B and #B is less than #C.

Does the relation "is complementary to" for angles have a reflexive property (consider one angle)? a symmetric property (consider two angles)? a transitive property (consider three angles)?

reflexive angles cannot be complementary. Symmetric angles can be complementary because two angles can add up to be 90 degrees. Transitive angle cannot be complementary because complementary is the combination of 2 angles not three.

Does the relation "is a brother of" have a reflexive property (consider one male)? a symmetric property (consider two males)? a transitive property (consider three males)?

reflexive brother, one cannot be his own brother. symmetric brother, yes because brother A is a brother to brother B. transitive brothers, Yes because brother A is a brother of Brother B and brother B is a brother of brother C therefore brother A and brother C are also brother.

Does the relation "is perpendicular to" have a reflexive property (consider line L)? a symmetric property (consider lines L and M)? a transitive property (consider lines L, M, and N)?

reflexive line cannot be perpendicular to itself. symmetric line can be perpendicular. transitive line cannot be perpendicular because there's no way to make 3 line perpendicular to each other.

Venn Diagrams

represent the law of detachment

bisector

separating into 2 congruent parts

If two parallel lines are cut by a transversal then the exterior angles on the same side of the transversal are ?

supplementary

If two parallel lines are cut by a transversal, then the interior angles side of the transversal are ?

supplementary

deduction (a law like 1+1=2)

the knowledge and acceptance of selected assumptions guarantee the truth of a particular conclusion

negation *also called logical complement*

the negation of a given statement P, denoted by ~P (which is read "NOT P"), makes a claim opposite that of the original statement. If the given statement is true, its negation is false, and vice versa

vertical angles

the nonadjacent angles formed by intersecting lines

Two triangles are congruent if the six parts of the first triangles is congruent to what?

to the six corresponding parts of the second triangles Note: the reverse is the same

a plane is ________ dimensional

two

congruent angles

two angles that have the same measure

supplementary angles

two angles whose sum is 180 degrees

complementary angles

two angles whose sum is 90 degrees

congruents angles

two angles with equal measure

opposite ray

two rays that share a common endpoint

parallel line

two straight line that never intersect

angle

union of two rays that share an endpoint

induction (if u see something that happen a lot u assumes that it will happen again)

using specific observation and experiments to draw a general conclusion