Discovering Geometry - Chapter 1.1 to 1.5 - Vocabulary
Point
The most basic building block of Geometry. A point has no size. It only has a location. You represent a point with a dot and a capital letter.
Base of an Isosceles Triangle
The side opposite the vertex angle
Base Angles of an Isosceles Triangle
The two (congruent) angles that are adjacent to the base of an isosceles triangle
Vertex
a point where rays or line segments meet
Equiangular Polygon
a polygon where all the angles have the same measure
Equilateral Polygon
a polygon where all the sides have the same measure
Concave Polygon
a polygon where at least one diagonal is outside the polygon
Octagon
a polygon with eight sides
Undecagon
a polygon with eleven sides
Regular Polygon
a polygon with equal angles and equal sides In other words, a polygon that is both equilateral and equiangular
Pentagon
a polygon with five sides
Quadrilateral
a polygon with four sides
n-gon
a polygon with n sides
Nonagon
a polygon with nine sides
Heptagon
a polygon with seven sides
Decagon
a polygon with ten sides
Triangle
a polygon with three sides.
Dodecagon
a polygon with twelve sides
Hexagon
a polygon with with six sides
Angle Bisector
a ray that contains the vertex of an angle and divides the angle into two congruent angles
Hexagon
a six-sided polygon
Scalene triangle
a triangle with no congruent sides
Right Triangle
a triangle with one angle of 90 degrees
Right angle
an angle whose measure is 90º
Obtuse angle
an angle whose measure is greater than 90º but less than 180º (between 90 and 180º)
Acute Angle
an angle whose measure is less than 90º but greater than 0º
Congruent Angles
angles that have the same measure
When forming a good definition, you should:
classify, differentiate, test (look for counterexample)
Vertex of a Polygon
each endpoint where the sides of a polygon meet
Side of a Polygon
each line segment that forms a polygon
Equal
having the same numerical value
Congruent
having the same size and shape
Equal
having the same value
Congruent
identical in shape and size; coinciding exactly when superimposed.
Parallel Lines
lines in the same plane that never intersect
Collinear
on the same line
Coplanar
on the same plane
Line Segment
part of a line that is bounded by two end points
Undefined terms of Geometry
point, line, and plane.
Congruent Polygons
polygons whose corresponding sides and angles have the same measure
Outgoing Angle
the angle formed between the path of a rebounding object and the surface it collided with, such as a billiard ball rolling toward a cushion or a ray of light traveling towards a mirror.
Incoming Angle
the angle formed between the path of an approaching object and the surface from which it rebounds, such as a billiard ball rolling toward a cushion or a ray of light traveling towards a mirror.
Reflex Measure of an Angle
the largest amount of rotation less than 360 degrees between the two rays of an angle
Midpoint of a segment
the point on the segment that is equidistant from the endpoints of the segment
Measure of an Angle
the smallest amount of rotation about a vertex from one ray to the other (between 0º and 180º)
Perimeter
the sum of the lengths of the sides of a polygon.
Sides of an Angle
the two non-collinear rays that make up an angle
Bisect
to divide into two equal parts
Isosceles triangle
triangle with at least two congruent sides
Vertical angles
two angles that are formed by intersecting lines. The angles share a vertex, but not a common side.
Linear Pair of Angles
two angles that share a vertex, a common side, and their non-common sides form a line.
Supplementary angles
two angles whose measures have a sum of 180º
Complementary angles
two angles whose measures have a sum of 90°
Skew lines
two lines that do not intersect and are non-coplanar
Perpendicular lines
two lines that intersect to form a right angle
Degree
unit for measuring angles
Things you can assume:
(1) lines are straight. (2) If two lines intersect, they intersect at one point. (3) points on a line are collinear and all points shown on a diagram are coplanar.
Things you can't assume:
(1) two lines are parallel just because they look parallel - they must be marked using parallel symbols (2) two lines are perpendicular just because they look perpendicular - they must be marked with a 90º symbol (3) pairs of angles, segments, or polygons are congruent - they must be marked with congruency symbols, which show that they're congruent
Convex Polygon
A polygon where no diagonal is outside the polygon
Definition
A statement that clarifies or explains the meaning of a word or a phrase.
Line
A straight continuous arrangements of infinitely many points. You represent a line by giving the letter names of any two points on the line and by placing a line symbol above the letters.
Plane
A surface with no thickness that extends infinitely along its length and width. You represent a plane with a four sided figure and by placing a script letter inside.
Acute Triangle
A triangle that contains only angles that are less than 90 degrees.
Obtuse Triangle
A triangle with one angle that is greater than 90 degrees.
Angle Addition
If C is on the interior of angle AOB then angle AOC + angle COB = angle AOB
Segment Addition
If points A, B, and C are collinear and B is between A and C, then AB + BC = AC.
Vertex Angle of an Isosceles Triangle
The angle formed by the legs of an isosceles triangle.
Polygon
a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others.
Angle
a figure formed by two rays or line segments that have a common endpoint. The two rays / segments can't be collinear.
Protractor
a geometry tool used to measure angles
Ray
a line extending in one direction from a point
Diagonal
a line segment that connects two nonconsecutive vertices of a polygon
