Math

Geometry

-it is the branch of math that studies shapes, sizes, lines, positions, angles, and spaces

Point

exact location, intersection, or a corner. It has no dimension , represented by a dot.

-named using a uppercase letter 

Line

-set of points that extend in both directions endlessly.

-named by the two points or a lowercase letter

Line Segment

Part of a line from one point to another point

Ray

-starts in one endpoint and continues endlessly in the other direction.

Plane

two dimensional, meaning it has height and length.

-requires three noncollinear lines to make it

Non-collinear

-Not on the same line

Angle

-formed when two rays meet at a common endpoint

Vertex

• - common endpoint

Acute angle

-less than 90 

Right angle

-exactly 90

Obtuse angle

-more than 90, less than 180

Straight angle

 

-exactly 180

Reflex angle

-more than 180

Parallel lines

-lines that dont meet and are equidistant

Equidistant

-is the same distant at a given point or line

Intersecting lines

-two lines having a common point

Transversal

-a line that cuts through two or more lines

Corresponding

-equal in measurement

Alternate Interior

-inside the parallel lines, opposite sides of the transversal

Alternate Exterior

-outside the parallel lines, opposite sides of the transversal

Same-side Interior

-inside the parallel lines and on the same side of the transversal

Same-side Exterior

-outside the parallel lines and on the same side of the transversal

Adjacent

Two angles that sit next to each other

Inductive

-specific details of observation to a general conclusion

Deductive

-general details of observation to a specific conclusion

-uses facts

Congruent triangles

• Two triangles that are the same shape and size

Corresponding parts

 the matching sides and angles between two geometric figures that sit in the same relative positions.

Vertical

-intersection of two lines

Included angle

-angle located directly between two given sides of a triangle

Included side

 -It is the specific side located directly between two given angles

Postulate 1

• A line is formed by at least two different points. A plane is formed by at least three noncollinear points. Space is formed by at least four noncoplanar points.

Postulate 2

• Through any two different points, there is exactly one line.

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Postulate 3

Through any three non collinear points, there is exactly one plane

Postulate 4

• two points lie in a plane, then the line containing these two points also lies in the same plane

Postulate 5

• If two different planes intersect, then the intersection is a line

Postulate 6

• There is a one-to-one correspondence between the points of a number line and the set of real numbers.

Postulate 7

• There is a unique distance between any two different points on the number line

Segment addition postulate

-three points A, B, and C are collinear, and AB + AC = AC, then B is between A and C

Congruent line segment

-two line segments have equal lengths, then they are congruent.

Midpoint of a line segment

-a point divides a line segment into two congruent segments

Bisector of a line segment

-a line, line segment, ray, or plane intersects a line segment at its midpoint, then it is called a bisector of the line segment.

Postulates

- Statements that are accepted as true; no need for a proof

Theorems

- Statements that require a proof before accepted as true

 Corresponding Parts of Congruent Triangles are Congruent.

CPCTC

Adjacent angles

Two angles that sit next to each other

Same-side, Exterior, Interior

Supplementary

Alternate, Corresponding

Congruent

Perpendicular line

Two lines that intersect and forms right angles

Corresponding parts

Pairs of side on angles of two triangles that are on the same position

Reflexive Property

a, a=a

Symmetric Property

a=b, then b=a

Transitive Property

a=b, b=c, then a=c

Substitution Property

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

Addition Property

   If a = b, then a + c = b + c

Subtraction Property

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

Multiplication Property

If a = b, then a x c = b x c

Division Property

If a = b, then a/c = b/c