Points Lines and Planes in Geometry is the lesson that many teachers skip or fly through because they “assume” (in huge air quotes) that the students know what these things are before they get to high school geometry. Unfortunately without a great understanding of points lines and planes, it’s almost impossible for them to grasp the tougher stuff.
Most students think that a point is something they can actually draw. They think you should be able to see it. They don’t understand that it is a location and not a dot on the paper with your pencil.
One great way to start your points lines and planes in geometry lesson is to tell them to actually draw a point either on their paper or have one student draw it on the board. Them ask a different student to measure the length and with of the point with a ruler. They will do it or try to do it and give actual numbers. Then you question them. If a point has no dimensions then how did you just give me measurements? This is where you explain that a point in geometry is a location. You can’t actually draw it because the second you put your pencil on paper you can measure it. This is a great place to transition into an explanation of what Dimensions are!
Points have no dimensions!A line has one dimension. So again you can’t really draw one because when you put your pencil on the paper it has a length and a width you can measure both. The lines you actually draw in geometry class are representations of lines. We can’t actually see them. Lines are used to measuring distance. A great way to show this to them is to have a really thin pencil and a really thick marker and tell two students to draw lines. They will visibly be able to see the thickness of the marker.
Lines are one dimensional!Planes are where things get fun. Now you are talking about space. Planes have a length and a width and are made up of infinitely many lines which are made of infinitely many points! What?
A Plane is a flat surface that has no start and no end in two dimensions. So can you actually draw one? Nope!
Planes are two dimensional!Don’t make it more confusing than it already is. Your lesson on [Dimensions] will greatly reduce the confusion about these three things. The better they understand dimensions the better they will understand Points, Lines, and Planes.
In geometry, some words, such as point, line, and plane, are undefined terms. Although these words are not formally defined, it is important to have a general agreement about what each word means.
A point has no dimension. It is usually represented by a small dot and named by a capital letter.
A line extends in one dimension. It is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions, and is named by two points on the line or a lowercase script letter.
A plane extends in two dimensions. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end, even though the drawing of a plane appears to have edges, and is named by a capital script letter or 3 non-collinear points.
A line segment is a set of points and has a specific length i.e. it does not extend indefinitely. It has no thickness or width, is usually represented by a straight line with no arrowheads to indicate that it has a fixed length, and is named by two points on the line segment with a line segment symbol above the letters.
A ray is a set of points and extends in one dimension in one direction (not in two directions). It has no thickness or width, is usually represented by a straight line with one arrowhead to indicate that it extends without end in the direction of the arrowhead, and is named by two points on the ray with a ray symbol above the letters.
Collinear points are points that lie on the same line.
Coplanar points are points that lie on the same plane.
Use the figure to name each of the following.
Two or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common.
Through any two points, there is exactly one line.
If two distinct lines intersect, then they intersect at exactly one point.
If two distinct planes intersect, then they intersect in exactly one line.
Through any three non-collinear points there is exactly one plane.
Refer to each figure.
Draw and label figure for each relationship.
