Geometry module 1.01
Module one-
Lesson 01.01
The terms point, line, and plane are referred to as undefined. When you write the definition of these terms, you have to rely on other terms that need defining.
Point- In general, a point is a location. Because points have no size, you can say they have no dimension.
Line- a "stream" of points that has no width or depth. You can also think of a line as points lined up next to each other that go on forever in opposite directions. Because you can measure the distance between points, lines have one dimension: length.
Collinear- Points on the same line.
Noncollinear- Points not on the same line.
Plane- a flat surface that extends indefinitely in all directions. Because two measurements can be made on a plane—the distance between two points on a line and the distance from a line to a point not on that line—planes have two dimensions: length and width.
Line Segment- A line segment is a portion of a line with two endpoints. Every point between and including the endpoints is part of the line segment.
Angle- a figure consisting of two noncollinear rays or segments with a common endpoint
Ray- part of a line that has one endpoint and continues in one direction infinitely.
Postulates- statements that mathematicians assume to be true without any proof to support them.
Ex: In the English alphabet, A comes before B. In math, you could draw a line through any two distinct points given.
Theorem- information that seem true but must be proven (like solving a mystery) using the postulates.
Ex: The Pythagorean theorem is proven true by using mathematical equations and postulates.
Points postulate- There is exactly one line through any two points. When given two points, you could draw a line through them.
Intersecting lines postulate- When two lines intersect, they intersect at exactly one point. Otherwise, it’s not a true line, or it’s the same line.
Intersecting planes postulate- When two planes intersect, they
Lesson 01.01
The terms point, line, and plane are referred to as undefined. When you write the definition of these terms, you have to rely on other terms that need defining.
Point- In general, a point is a location. Because points have no size, you can say they have no dimension.
Line- a "stream" of points that has no width or depth. You can also think of a line as points lined up next to each other that go on forever in opposite directions. Because you can measure the distance between points, lines have one dimension: length.
Collinear- Points on the same line.
Noncollinear- Points not on the same line.
Plane- a flat surface that extends indefinitely in all directions. Because two measurements can be made on a plane—the distance between two points on a line and the distance from a line to a point not on that line—planes have two dimensions: length and width.
Line Segment- A line segment is a portion of a line with two endpoints. Every point between and including the endpoints is part of the line segment.
Angle- a figure consisting of two noncollinear rays or segments with a common endpoint
Ray- part of a line that has one endpoint and continues in one direction infinitely.
Postulates- statements that mathematicians assume to be true without any proof to support them.
Ex: In the English alphabet, A comes before B. In math, you could draw a line through any two distinct points given.
Theorem- information that seem true but must be proven (like solving a mystery) using the postulates.
Ex: The Pythagorean theorem is proven true by using mathematical equations and postulates.
Points postulate- There is exactly one line through any two points. When given two points, you could draw a line through them.
Intersecting lines postulate- When two lines intersect, they intersect at exactly one point. Otherwise, it’s not a true line, or it’s the same line.
Intersecting planes postulate- When two planes intersect, they