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
Quadrant
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
Transformation
Translation
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
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
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)
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.