Early uses of solid geometry.
Early uses of solid geometry.
 Early uses of solid geometry.
Early uses of solid geometry.
 Early uses of solid geometry.
Early uses of solid geometry.
 Early uses of solid geometry.
Early uses of solid geometry.
 Figures of solid geometry.
Figures of solid geometry.
 Figures of solid geometry.
Figures of solid geometry.
 Figures of solid geometry.
Figures of solid geometry.
 Figures of solid geometry.
Figures of solid geometry.
 The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
 The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
 The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
 The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
 Exact definition of a plane.
Exact definition of a plane.
 Exact definition of a plane.
Exact definition of a plane.
 Exact definition of a plane.
Exact definition of a plane.
 Exact definition of a plane.
Exact definition of a plane.
 The Use of the Word "Determine".
The Use of the Word "Determine".
 The Use of the Word "Determine".
The Use of the Word "Determine".
 The Use of the Word "Determine".
The Use of the Word "Determine".
 The Use of the Word "Determine".
The Use of the Word "Determine".
 How a plane is determined.
How a plane is determined.
 How a plane is determined.
How a plane is determined.
 How a plane is determined.
How a plane is determined.
 How a plane is determined.
How a plane is determined.
 Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
 Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
 Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
 Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
 Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
 Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
 Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
 Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
 Intersection.
Intersection.
 Intersection.
Intersection.
 Intersection.
Intersection.
 Intersection.
Intersection.
 Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
 Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
 Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
 Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
 The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
A line perpendicular to a plane.
A line perpendicular to a plane.
 A line perpendicular to a plane.
A line perpendicular to a plane.
 A line perpendicular to a plane.
A line perpendicular to a plane.
 A line perpendicular to a plane.
A line perpendicular to a plane.
 If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
 If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
 If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
 If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
 Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
 Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
 Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
 Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
 Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
 Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
 Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
 Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
 Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
 Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
 Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
 Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Early uses of solid geometry.
Early uses of solid geometry.
Early uses of solid geometry.
Early uses of solid geometry.
Early uses of solid geometry.
Early uses of solid geometry.
Early uses of solid geometry.
Early uses of solid geometry.
Figures of solid geometry.
Figures of solid geometry.
Figures of solid geometry.
Figures of solid geometry.
Figures of solid geometry.
Figures of solid geometry.
Figures of solid geometry.
Figures of solid geometry.
The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
The axioms and postulates of plane geometry.
Exact definition of a plane.
Exact definition of a plane.
Exact definition of a plane.
Exact definition of a plane.
Exact definition of a plane.
Exact definition of a plane.
Exact definition of a plane.
Exact definition of a plane.
The Use of the Word "Determine".
The Use of the Word "Determine".
The Use of the Word "Determine".
The Use of the Word "Determine".
The Use of the Word "Determine".
The Use of the Word "Determine".
The Use of the Word "Determine".
The Use of the Word "Determine".
How a plane is determined.
How a plane is determined.
How a plane is determined.
How a plane is determined.
How a plane is determined.
How a plane is determined.
How a plane is determined.
How a plane is determined.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Postulate 20. (1) A straight line and an outside point determine a plane. (2) Three non-collinear points determine a plane. (3) Two intersecting lines determine a plane.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Points that lie on the same straight line are said to be collinear. Points that lie on the same plane are said to be coplanar.
Intersection.
Intersection.
Intersection.
Intersection.
Intersection.
Intersection.
Intersection.
Intersection.
Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
Postulate 21. If two planes intersect, they have at least two points in common.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
The Intersection of two lines.
A line perpendicular to a plane.
A line perpendicular to a plane.
A line perpendicular to a plane.
A line perpendicular to a plane.
A line perpendicular to a plane.
A line perpendicular to a plane.
A line perpendicular to a plane.
A line perpendicular to a plane.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
If a line is perpendicular to each of two intersecting lines at their point of intersection, it is perpendicular to the plane according to the lines.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 1. A plane can be drawn perpendicular to a given line at a given point on the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 2. Only one plane can be drawn perpendicular to a given line at a given point of the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
Corollary 3. A plane can be drawn perpendicular to a given line on a given point not in the line.
info
prev / next