Geometry Exam

collinear

points that lie on the same line

noncollinear

points that don't lie on the same line

Coplanar

lines that lie on the same plane

Concurrent

lines that intersect

ray

a definite start and no definite ending

angle

a pair of rays that have the same end point

Triangle

A polygon that has 3 sides

Quadrilateral

A polygon that has 4 sides

Pentagon

A polygon that has 5 sides

Octagon

A polygon that has 8 sides

Commutative

a+b=b+a
ab=ba

Associative

(a+b)+c=a+(b+c)
(ab)c=a(bc)

Additive Identity

a+0=a

Additive Inverse

a+(-a)=0

Multiplicative Inverse

a*(1/a)=1

Converse

reversing the hypothesis and conclusion

Conjunction and table

p and q

Disjunction

p or q

Syllogism

a-->b, b-->c, a-->c

Theorem

statement that is proved by reasoning deductively from already accepted statements

Premise

a-->b,b-->c, c-->d

An Indirect Proof

If not d, then e if e, then f and so on, until we come to a contradiction therefore, not d is false, so d is true

Postulate

Axium

Acute Angle

Angle less then 90 degrees

Obtuse Angle

Angle more then 90 degress

Straight Angle

180 degrees

Right Angle

90 degrees

Corollary

A theorem that can be easily proved as a consequence of a definition a postulate or another theorem

Complementary

2 angles that sum to 90

Supplementary

2 angles that sum to 180

Linear Pairs

2 angles that have a common side and whose other sides are opposite rays

Vertical Angles

2 angles such that the sides of one angle are opposite rays to the sides of the other

Perpendicular

Lines that form a right angle

Polygon

A connected set of at least 3 line segments in the same plane such that each segment intersects exactly 2 others one at each endpoint

Congruent Triangles

2 triangles for which there is a correspondence between their vertices such that all their corresponding sides and angles are equal

ASA

When there are 2 triangles and a pair of angles are equal, pair of sides are equal and finally a pair of angles are equal

SAS

When there are 2 triangles and a pair of sides are equal, pair of angles are equal and finally a pair of sides are equal

Scalene

iff has no equal sides

Isosceles

iff 2 of its sides are equal

Equilateral

iff all of the sides are equal

Obtuse

Iff one angle is more than 90 degrees

Right

iff one of the 3 angles are 90 degrees

Acute

iff all 3 angles are acute

Equiangular

all angles are equal, meaning angles are 60 degrees

Three Possibilities Property

a>b, a=b, b>a

Transitive Property

a>b and b>c then a>c

Addition Property

a>b then a+c>a+b

Subtraction Property

a>b then a-c>a-b

Multiplication Property

a>b, c>0 then ac>bc

Division Property

a>b, c>0 then a/c>b/c

Addition Theorem of Inequality

a>b and c>d, a+c>b+d

Whole Greater than Part

a>0, b>0 and a+b=c, then c>a and c>b

Exterior Angle of a Triangle

An exterior angle of a triangle is greater than either remote interior angle

Parallel lines

lines that lie in the same plane and do not intersect

Transversal

A line that intersects 2 or more lines that lie in the same plane in different points

Corresponding Angles

angles on the same side of a transversal on 2 separate lines in the same position

Alternate Interior Angles

angles on opposite sides of the transversal, in the interior region of 2 lines, on 2 different lines

Alternate Exterior Angles

angles on opposite sides of the transversal, in the exterior region of 2 lines, on 2 different lines

Consecutive Interior Angles

angles on the same side of the transversal in the interior region of 2 lines on 2 different lines

Parallelogram

a quadrilateral whose opposite sides are parallel

A Square

a quadrilateral all of whose sides and angles are equal

A Rhombus

a quadrilateral all whose sides are equal

A Trapezoid

a quadrilateral that has exactly one pair of parallel sides

An Isosceles Trapezoid

A trapezoid whose legs are equal

A Midsegment of a Triangle

A line segment that connects the midpoints of 2 of a triangles sides

A Polygonal Region

The Union of a polygon and its interior

AA Similarity

If 2 angles of one triangle are equal to 2 angles of another triangle, then the triangles are similar