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)

Image: Ordered Pair
Angle & Coordinate Plane - Geometry

X-Coordinate

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

Image: X-Coordinate
Angle & Coordinate Plane - Geometry

Y-Coordinate

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

Image: Y-Coordinate
Angle & Coordinate Plane - Geometry

Quadrant

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

Image: Quadrant
Angle & Coordinate Plane - Geometry

Origin

The point at which the axes intersect.

Image: Origin
Angle & Coordinate Plane - Geometry

Congruent

Geometric figures that have exactly the same shape and size.

Image: Congruent
Angle & Coordinate Plane - Geometry

Midpoint

The point halfway between the endpoints of the segment.

Image: Midpoint

Segment Bisector

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

Image: Segment Bisector

Angle

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

Image: Angle

Vertex

The common endpoint of an angle

Image: Vertex

Angle Bisector

A ray that divides an angle into two congruent angles

Image: Angle Bisector

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

Image: Plane

Collinear

Points that lie on the same line.

Image: Collinear

Coplanar

Points that lie in the same plane

Image: Coplanar

Intersection

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

Image: Intersection

Space

A Boundless 3-D set of all points


Parallel

Lines, segments, rays or planes that never intersect

Image: Parallel

Perpendicular

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

Image: Perpendicular

Parallel

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

Image: Parallel Lines

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

Image: Interior Angles

Exterior Angles

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

Image: Exterior Angles

Alternate Interior Angles

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

Image: Alternate Interior Angles

Corresponding Angles

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

Image: Corresponding Angles

Alternate Exterior Angles

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

Image: Alternate Exterior Angles

Congruent segments

line segments whose lengths are equal

Image: Congruent segments

Horizontal Reflectional (Line) Symmetry

reflectional symmetry about a horizontal line of reflection

Image: Horizontal Reflectional (Line) Symmetry

Midpoint of a Line Segment

the point halfway between the endpoints of a line segment

Image: Midpoint of a Line Segment

Perpendicular Lines

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

Image: Perpendicular Lines

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)

Image: Reflection

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

Image: Transformation

Translation

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

Image: Translation

Two-Dimensional Coordinate System

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

Image: Two-Dimensional Coordinate System

Perpendicular Bisector

a perpendicular segment that bisects a segment

Image: Perpendicular Bisector

Concurrent LInes

when three or more lines intersect at a common point

Image: Concurrent LInes

Point of Concurrency

the point where concurrent lines intersect

Image: Point of Concurrency

Circumcenter

the point where perpendicular bisectors of a triangle are concurrent

Image: Circumcenter

Incenter

the point where angle bisectors of a triangle are concurrent

Image: Incenter

Median

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

Image: Median

Centroid

the point where the medians of a triangle are concurrent

Image: Centroid

Altitude

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

Image: Altitude

Orthocenter

the point where the altitudes of a triangle are concurrent

Image: Orthocenter

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

Angle & Coordinate Plane - Geometry

line segment

part of a line with two endpoints

Angle & Coordinate Plane - Geometry

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


adjacent 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)

Angle & Coordinate Plane - Geometry

distance

the length between two points

Angle & Coordinate Plane - Geometry

midpoint

A point that divides a segment into two congruent segments


concave

polygon with a “dent” or “caved in”

Angle & Coordinate Plane - Geometry

convex

polygon with no “dents”

Angle & Coordinate Plane - Geometry

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

Angle & Coordinate Plane - Geometry

alternate interior angles

Interior angles that lie on opposite sides of the transversal

Angle & Coordinate Plane - Geometry

alternate exterior angles

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

Angle & Coordinate Plane - Geometry

corresponding angles

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

Angle & Coordinate Plane - Geometry

vertex angle

The angle formed by the legs of an isosceles triangle.


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