Geometry in Our WorldGeometry in Our World

By Lola, Gillian, and GraceBy Lola, Gillian, and Grace

Two Lines Are Coplanar: SometimesTwo Lines Are Coplanar: Sometimes

The guitar neck represents a The guitar neck represents a plane. The strings represent lines plane. The strings represent lines on that plane. This is an example on that plane. This is an example

of when this statement is true.of when this statement is true.

This highway intersection represent This highway intersection represent two planes. One line is on each plane two planes. One line is on each plane showing that two lines are not always showing that two lines are not always

coplanar.coplanar.

A Line Intersects a Plane in One Point: A Line Intersects a Plane in One Point: SometimesSometimes

The pencil (line) is going through the The pencil (line) is going through the paper (plane). They intersect in a paper (plane). They intersect in a

single point.single point.

The road shows a line that intersects The road shows a line that intersects a plane at infinite points, or in a line.a plane at infinite points, or in a line.

Two Planes Intersect in a Line: Two Planes Intersect in a Line: SometimesSometimes

The sides of the fence each The sides of the fence each represent one plane and they represent one plane and they

intersect in a line at the intersect in a line at the corner of the fence.corner of the fence.

These two shelves represent two These two shelves represent two parallel planes. Because they are parallel planes. Because they are parallel they will never intersect.parallel they will never intersect.

Two Planes Intersect in a Single Point: NeverTwo Planes Intersect in a Single Point: Never

Because two planes go on forever, they are infinite Because two planes go on forever, they are infinite which means that if they intersect, they will always which means that if they intersect, they will always

intersect in infinite points, or a line.Three planes can intersect in infinite points, or a line.Three planes can intersect in a point, because there is only one point intersect in a point, because there is only one point that they all would intersect, but every plane would that they all would intersect, but every plane would

intersect with one of the others in a line.intersect with one of the others in a line.

Planes Have an Edge: NeverPlanes Have an Edge: Never

Planes don’t have edges because they Planes don’t have edges because they go on infinitely. Planes are only drawn go on infinitely. Planes are only drawn with edges so that they are easier to with edges so that they are easier to

visualize.visualize.

Two Points Are Collinear: AlwaysTwo Points Are Collinear: Always

The two birds each represent a point The two birds each represent a point on the line (wire). You can always draw on the line (wire). You can always draw

a line between any two points no a line between any two points no matter where they are placed on a matter where they are placed on a

plane.plane.

Three Point Are Collinear: SometimesThree Point Are Collinear: Sometimes

Orion’s Belt shows three Orion’s Belt shows three points, the stars, all in a points, the stars, all in a

line. line.

You can’t draw a line You can’t draw a line through all three stones, through all three stones,

or points, on this plane, or or points, on this plane, or beach. Therefore they are beach. Therefore they are

not collinear.not collinear.

Three Points Are Coplanar: AlwaysThree Points Are Coplanar: Always

The three raindrops, points, are all on the The three raindrops, points, are all on the window or plane. No matter where any three window or plane. No matter where any three

points are placed you can always angle a points are placed you can always angle a plane to make all three coplanar. plane to make all three coplanar.

Sometimes all four of the Sometimes all four of the horses hooves, or points, are horses hooves, or points, are

on the ground, or plane. on the ground, or plane. Therefore they are coplanar.Therefore they are coplanar.

Four Points are Coplanar: SometimesFour Points are Coplanar: Sometimes

This horse is rearing and two of This horse is rearing and two of his hooves are not on the his hooves are not on the

ground. Therefore all four of his ground. Therefore all four of his hooves are not coplanar.hooves are not coplanar.

A Point is a Small, Filled CircleA Point is a Small, Filled Circle

THIS IS NOT A POINT!THIS IS NOT A POINT!

A point has zero dimensions, and is actually A point has zero dimensions, and is actually invisible. A very small filled circle is used to invisible. A very small filled circle is used to represent a point because people can’t draw represent a point because people can’t draw

something with zero dimensions. A small filled something with zero dimensions. A small filled circle has two dimensions, therefore can not be a circle has two dimensions, therefore can not be a

real point. real point.