Discovering Geometry - Chapter 1.1 to 1.5 - Vocabulary

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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


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