# Angle & Coordinate Plane – Geometry

### Angle & Coordinate Plane – Geometry Basics

This chapter is about basics of Geometry including coordinate plane, angle, quadrant & congruent etc.

Ordered Pair

Points on the coordinate plane (x,y)

X-Coordinate

The first number in an ordered pair that correspongs to a number on the x-axis

Y-Coordinate

The second number in an ordered pair that corresponds to a number on the y-axis

The four regions of the coordinate plane created by the x-axis and y-axis

Origin

The point at which the axes intersect.

Congruent

Geometric figures that have exactly the same shape and size.

Midpoint

The point halfway between the endpoints of the segment.

##### Segment Bisector

Any segment, line or plane that intersects a segment at it’s midpoint.

Angle

Formed by two non-collinear rays that have a common endpoint

Vertex

The common endpoint of an angle

Angle Bisector

A ray that divides an angle into two congruent angles

Point

A location – it has neither shape nor size

Line

Made up of points and has no thickness or width.

Plane

A flat surface made up of points that extends infinitely in all directions

Collinear

Points that lie on the same line.

Coplanar

Points that lie in the same plane

Intersection

The set of points two or more geometric figures have in common.

Space

A Boundless 3-D set of all points

Parallel

Lines, segments, rays or planes that never intersect

Perpendicular

Lines, segments,rays or planes that form right angles.

Parallel

LinesCoplanar lines that do not intersect. Their slopes are equal.

Transversal

A line that intersects two or more lines in a plane at different

pointsInterior

AnglesAngles that lie between two transversal that intersect the same line

##### Exterior Angles

An angle formed by one side of triangle and the extension of another side

Alternate Interior Angles

Angles that are on opposite sides of the transversal and are in between the parallel lines

Corresponding Angles

Angles that are in the same position, but a different group of angles

Alternate Exterior Angles

Angles that are on opposite sides of the transversal and are outside the parallel lines

Congruent segments

line segments whose lengths are equal

Horizontal Reflectional (Line) Symmetry

reflectional symmetry about a horizontal line of reflection

Midpoint of a Line Segment

the point halfway between the endpoints of a line segment

Perpendicular Lines

lines in the same plane that intersect at 90 angles whose slopes are opposite reciprocals,

Reflection

rigid transformation in which each point in a geometric figure is at an equal distance on the opposite side of a given line (line of symmetry)

Transformation

one to one mapping of points in a plane such that each point in the pre-image has a unique image and each point in the image has a pre-image

##### Translation

rigid transformation moving all points in a geometric figure the same distance and the same direction

Two-Dimensional Coordinate System

two axes at right angles to each other, forming a xy-plane, consisting of points (x, y)

Perpendicular Bisector

a perpendicular segment that bisects a segment

Concurrent LInes

when three or more lines intersect at a common point

Point of Concurrency

the point where concurrent lines intersect

Circumcenter

the point where perpendicular bisectors of a triangle are concurrent

Incenter

the point where angle bisectors of a triangle are concurrent

Median

a segment that connects a vertex of a triangle with the midpoint of the opposite side

Centroid

the point where the medians of a triangle are concurrent

Altitude

a segment from a vertex perpendicular to the opposite side of a triangle (can be outside the triangle)

Orthocenter

the point where the altitudes of a triangle are concurrent

point

a location

line

made up of points and has no thickness or width

plane

a flat surface that extends forever in all directions

Noncollinear

points that do not lie on the same line

Collinear

points that lie on the same line

Noncoplanar

points that do not lie on the same plane

Coplanar

points that lie on the same plane

congruent

Having the same measure

##### line segment

part of a line with two endpoints

angle

amount of rotation between two lines (or rays) around a common point (vertex)

angle bistector

ray or line that divides an angle into two congruent angles

Two angles next to each other that share a common side and have the same vertex

supplementary angles

two angles that add up to 180 degrees

complementary angles

two angles that add up to 90 degrees

vertical angles

the angles opposite each other when two lines cross

perpendicular lines

Two lines that intersect to form right angles (90 degrees)

distance

the length between two points

midpoint

A point that divides a segment into two congruent segments

concave

polygon with a “dent” or “caved in”

convex

polygon with no “dents”

regular polygon

a polygon that is both equilateral and equiangular

equilateral triangle

A triangle with 3 congruent sides and 3 congruent angles.

Equiangular

all angles are congruent

isosceles triangle

a triangle with two congruent sides and two congruent angles

scalene triangle

a triangle with no congruent sides

consecutive interior angles

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

alternate interior angles

Interior angles that lie on opposite sides of the transversal

alternate exterior angles

Angles that lie outside a pair of lines and on opposite sides of a transversal.

corresponding angles

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

vertex angle

The angle formed by the legs of an isosceles triangle.

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