📚 Geometry - Chapter 1: Tools of Geometry 📚
1.1 Understanding Points, Lines, and Planes
🔹 Undefined Terms in Geometry
In geometry, there are three fundamental terms that are considered
undefined because they are only described using examples and
descriptions rather than formal definitions.
1. Point
o A point is a location in space.
o It has no size, width, or thickness.
o It is represented by a dot and named with a capital letter.
o Example: Point A (written as A).
2. Line
o A line is a straight path that extends infinitely in both directions.
o It has no thickness.
o A line is named using two points on the line or a lowercase
script letter.
o Example: Line AB (written as AB or BA), or line ℓ.
3. Plane
o A plane is a flat surface that extends infinitely in all directions.
o It has no depth.
o Named with a script letter or three non-collinear points.
o Example: Plane M or Plane XYZ (as long as X, Y, and Z are
non-collinear).
🔹 Collinear and Coplanar
Collinear Points → Points on the same line.
Coplanar Points → Points on the same plane.
✨ Real-Life Examples of Points, Lines, and Planes ✨
, Conce
Real-Life Example
pt
A dot on a piece of paper, the tip
Point
of a pen
Line A laser beam, a pencil edge
A desktop, the surface of a
Plane
whiteboard
🔹 Intersections in Geometry
1. Two lines intersect at a point.
2. A line and a plane intersect at a point.
3. Two planes intersect at a line.
✏️
Example:
Imagine two roads crossing—the intersection is a point.
The ceiling and a wall intersect in a line.
A tabletop represents a plane.
1.2 Measuring Line Segments and Precision
🔹 Line Segments and Their Measures
A line segment is part of a line that has two endpoints.
Notation: Segment AB is written as AB (no line above it).
Measuring Segments
To measure a line segment:
1. Identify the two endpoints.
2. Use a ruler or a given coordinate system.
3. Apply segment addition when necessary.
🔹 Segment Addition Postulate
If point B is between A and C, then:
AB+BC=ACAB + BC = AC
1.1 Understanding Points, Lines, and Planes
🔹 Undefined Terms in Geometry
In geometry, there are three fundamental terms that are considered
undefined because they are only described using examples and
descriptions rather than formal definitions.
1. Point
o A point is a location in space.
o It has no size, width, or thickness.
o It is represented by a dot and named with a capital letter.
o Example: Point A (written as A).
2. Line
o A line is a straight path that extends infinitely in both directions.
o It has no thickness.
o A line is named using two points on the line or a lowercase
script letter.
o Example: Line AB (written as AB or BA), or line ℓ.
3. Plane
o A plane is a flat surface that extends infinitely in all directions.
o It has no depth.
o Named with a script letter or three non-collinear points.
o Example: Plane M or Plane XYZ (as long as X, Y, and Z are
non-collinear).
🔹 Collinear and Coplanar
Collinear Points → Points on the same line.
Coplanar Points → Points on the same plane.
✨ Real-Life Examples of Points, Lines, and Planes ✨
, Conce
Real-Life Example
pt
A dot on a piece of paper, the tip
Point
of a pen
Line A laser beam, a pencil edge
A desktop, the surface of a
Plane
whiteboard
🔹 Intersections in Geometry
1. Two lines intersect at a point.
2. A line and a plane intersect at a point.
3. Two planes intersect at a line.
✏️
Example:
Imagine two roads crossing—the intersection is a point.
The ceiling and a wall intersect in a line.
A tabletop represents a plane.
1.2 Measuring Line Segments and Precision
🔹 Line Segments and Their Measures
A line segment is part of a line that has two endpoints.
Notation: Segment AB is written as AB (no line above it).
Measuring Segments
To measure a line segment:
1. Identify the two endpoints.
2. Use a ruler or a given coordinate system.
3. Apply segment addition when necessary.
🔹 Segment Addition Postulate
If point B is between A and C, then:
AB+BC=ACAB + BC = AC
