Basics of Geometry, Undefined Terms, and Segment Properties

Flashcards covering basic geometric undefined and defined terms, angle classifications, Ruler Postulate, and Segment Addition Postulate from Lesson 1-1.

What are undefined terms in geometry?

Terms whose meanings are accepted without formal definition and serve as the basic building blocks of geometry.

What are the three undefined terms identified in the geometry notes?

Point, line, and plane.

How is a point defined in the geometry vocabulary notes?

An exact location in space, represented by a dot.

What is the definition of a line?

A connected straight path that goes on forever in both directions.

What is the definition of a plane?

A flat surface that goes on forever in all directions, extending without end and having no thickness.

What is a line segment?

Part of a line that consists of two endpoints and all points between them.

What is an endpoint?

A point at the end of a line segment, or the start of a ray.

What is a ray?

A part of a line that starts at an endpoint and goes on forever in one direction.

What are opposite rays?

Rays with the same endpoint that lie on the same line.

How is an angle defined in the geometry notes?

A figure formed by two rays with a common endpoint called a vertex, where each ray forms a side of the angle.

What are collinear points?

Points that all lie on the same line.

What is the geometric definition of congruent?

Having the same size and shape.

How is an acute angle classified?

An angle that measures less than $90^\text{degrees}$.

How is a right angle defined?

An angle that measures exactly $90^\text{degrees}$.

How is an obtuse angle classified?

An angle that measures more than $90^\text{degrees}$.

What is Postulate 1-1 (Ruler Postulate)?

Every point on a line can be paired with a unique real number called its coordinate, and the distance between any two points is the absolute value of the difference of their coordinates.

How is the distance between two points $X$ and $Y$ calculated using Postulate 1-1?

The distance is $XY = |x_1 - x_2|$ or $XY = |x_2 - x_1|$, where $x_1$ and $x_2$ are the coordinates of $X$ and $Y$.

What is Postulate 1-2 (Segment Addition Postulate)?

If points $A$, $B$, and $C$ are on the same line with $B$ between $A$ and $C$, then $AB + BC = AC$.

In Example 3, if collinear points $J$, $K$, and $L$ have lengths $JK = 3n$, $KL = 5n - 7$, and $JL = 25$, what is the value of $n$?

$$n = 4$$

In Example 3, using $n = 4$, what are the lengths of $JK$ and $KL$?

$JK = 12$ and $KL = 13$