Introduction to Geometry by Samuel Chukwuemeka (Samdom For Peace) Points, Lines, and Planes

A point is an exact location in space. It has no size. You are here.

A true point has no length, no width, and no height. In fact, you cannot see a true point.

A point is named by a letter. P Point P

Lines are series of points that extends in opposite directions without end. Lines continue forever in both directions.

Because a line has no width or height, you cannot see a true line.

A line is defined by 2 points. A B Line AB

A ray is part of a line that has a starting point but no ending point.

A ray of light has a starting point (like the sun) and continues forever in the same direction.

Of course, if the ray hits an object, the light could be absorbed or reflected. MIRROR

A ray is also defined by 2 points. C D Ray CD

A line segment is part of a line that has a starting point and an ending point. Line segments can be measured.

A line segment also defined by 2 points. E F Line Segment EF

Lines can do various things.

Lines can intersect at a point to form angles. Two lines intersect if they have exactly one point in common. Lines that intersect are called Intersecting Lines. X Y Z

So, an Angle is formed when two lines meet or intersect. Angles are defined by 3 points. X Z Y XYZ

These angles can be right angles. 90 

These angles can be right angles. c R S T U V RST = 90 ⁰ USR = 90 ⁰ USV = 90 ⁰ TSV = 90 ⁰

When lines intersect to form right angles, they are said to be perpendicular. V R T U c S UTRV

Lines can also intersect to form acute and obtuse angles. 135  obtuse 45  acute

Lines can also run into each other to form straight angles.

180  is a straight angle

Lines do not always intersect.

Lines can also be parallel. Parallel lines are lines that lie on the same plane and do not intersect.

Parallel lines have the same slope or steepness.

Is it possible for lines not to intersect and not be parallel either?

Believe it or not, this is possible. Let’s consider a 3-dimensional rectangular prism.

These 2 lines are not parallel, but they are not intersecting either.

These lines are called skew lines. Skew lines are lines that do not lie in the same plane and do not intersect.

You might have heard the word “skewer” the last time you had a barbecue. SKEWERSKEWER

A skewer raises your “dinner” off the surface of the grill. The skewer does not intersect the grill, and the skewer is not parallel to the grill.

Lines can be… intersecting perpendicular 90º parallel skew

A plane is a flat surface that has length & width but no height.

You can see a plane only if you view it at a certain angle.

A true plane goes on forever in all directions.

Planes can…

Planes can intersect.

An X-Wing fighter from Star Wars has wings that intersect.

Planes can be perpendicular.

Planes can be parallel.

A Tie Fighter from Star Wars has wings that are parallel.

Planes can be… intersecting perpendicular parallel

Assignment In a tabular form, (1.) Differentiate between a point, a line, a plane, a segment, and a ray. (2.) Differentiate between intersecting, parallel, and skew lines (3.) Define a perpendicular line

Sweethearts and Gentlemen, ask your questions.