Question

basic definitions & notation date: name picture definition notation point • g line ←→ a b ray → j k ← l m line segment or segment — x y angle a b c intersect b c d ↓ a parallel f e → h ← g perpendicular l↑ n← → o m↓

Answer:

To fill in the "Definition" and "Notation" columns for each geometric term, we use standard geometric definitions and notations:

1. Point

Step1: Define a Point

A point is a location in space with no size (no length, width, or height).

Step2: Notation for a Point

A point is denoted by a capital letter (e.g., the point in the picture is \( G \), so notation is \( G \)).

2. Line

Step1: Define a Line

A line is a straight path that extends infinitely in both directions, with no thickness. It contains infinitely many points.

Step2: Notation for a Line

A line can be denoted by two points on it with a double - headed arrow: \( \overleftrightarrow{AB} \) (for the line through points \( A \) and \( B \)).

3. Ray

Step1: Define a Ray

A ray is a straight path that starts at a point (the endpoint) and extends infinitely in one direction.

Step2: Notation for a Ray

For ray \( JK \) (endpoint \( J \), extending through \( K \)): \( \overrightarrow{JK} \); for ray \( LM \) (endpoint \( L \), extending through \( M \)): \( \overleftarrow{LM} \).

4. Line Segment (or Segment)

Step1: Define a Line Segment

A line segment is a part of a line with two endpoints. It has a definite length.

Step2: Notation for a Line Segment

A line segment is denoted by its two endpoints with a bar: \( \overline{XY} \) (for the segment with endpoints \( X \) and \( Y \)).

5. Angle

Step1: Define an Angle

An angle is formed by two rays (or line segments) with a common endpoint (the vertex). It measures the amount of rotation between the two rays.

Step2: Notation for an Angle

If the vertex is \( B \) and the rays are \( BA \) and \( BC \), the angle is denoted as \( \angle ABC \) (or \( \angle B \)).

6. Intersect

Step1: Define Intersect

Two lines (or rays, or segments) intersect if they cross each other at a point.

Step2: Notation for Intersect

If lines \( AB \) and \( CD \) intersect, we write \( AB \cap CD=\text{[intersection point]} \) (e.g., if they intersect at a point, say \( P \), then \( AB \cap CD = P \)).

7. Parallel

Step1: Define Parallel

Two lines (or rays, or segments) are parallel if they lie in the same plane and never intersect, no matter how far they are extended.

Step2: Notation for Parallel

If lines \( EF \) and \( GH \) are parallel, we write \( EF \parallel GH \).

8. Perpendicular

Step1: Define Perpendicular

Two lines (or rays, or segments) are perpendicular if they intersect at a right angle ( \( 90^\circ \) ).

Step2: Notation for Perpendicular

If lines \( LM \) and \( NO \) are perpendicular, we write \( LM \perp NO \).

Filled Table (Summary)

Name	Picture	Definition	Notation
Line	\( \boldsymbol{\overleftrightarrow{AB}} \)	A straight path extending infinitely in both directions.	\( \overleftrightarrow{AB} \)
Ray	\( \boldsymbol{\overrightarrow{JK}}, \boldsymbol{\overleftarrow{LM}} \)	A path starting at an endpoint and extending infinitely in one direction.	\( \overrightarrow{JK}, \overleftarrow{LM} \)
Line Segment or Segment	\( \boldsymbol{\overline{XY}} \)	A part of a line with two endpoints (definite length).	\( \overline{XY} \)
Angle	\( \boldsymbol{\angle ABC} \) (with vertex \( B \))	Formed by two rays with a common vertex (measures rotation).	\( \angle ABC \) (or \( \angle B \))
Intersect	Lines \( AB, CD \) crossing	Two figures cross at a point.	\( AB \cap CD = \text{[point]} \)
Parallel	\( \boldsymbol{EF \parallel GH} \)	Lines in the same plane that never intersect.	\( EF \parallel GH \)
Perpendicular	\( \boldsymbol{LM \perp NO} \)	Lines intersecting at a \( 90^\circ \) angle.	\( LM \perp NO \)

(Note: For the "Intersect" row, the specific intersection point can be named based on the diagram, but the general notation for intersection is shown above.)