Intro to Euclidean Geometry
Coordinate Plane Review
For more detailed review of coordinate planes and ordered pairs with examples, refer to the 6th Grade Math: Euclidean/Coordinate Plane, Ordered Pairs page
What is a coordinate plane?
A coordinate plane is a system that uses one or numbers (coordinates) to determine a position of a point.
The left-right (horizontal) direction is known as x (referred to as the x-axis).
The up-down (vertical) direction is known as y (referred to as the y-axis).
However, that coordinate grid is just two-dimensional. It is possible for there to be a 3rd dimension in geometry -- this is where the z-axis comes in.
(x,y,z) = 3 coordinates to define a point
Try visualizing it!
Watch the video
Use pencils and paper to imitate the behavior of the 3 planes
Terms and Labels
Point – an exact location in space. A point has no dimension
Line Segment – a part of a line having two endpoints.
Line – a collection of points along a straight path that extends endlessly in both directions
Ray – a part of a line having only one endpoint
Angle – consists of two rays that have a common. The endpoint called the vertex of the angle.
Plane – a flat surface that extends endlessly in all directions.
Collinear - lying in the same straight line
Coplanar - lying on the same plane
Watch the video for a good review of what we just learned!
Supplementary vs Complementary Angles
Angles are supplementary if the sum of their angles is 180 degrees (make up a straight angle!)
Angles are complementary if the sum of their angles is 90 degrees (make up a right angle!)
If two angles are complementary and one of them is 52 degrees, what is the other one? Answer: 32 degrees (90-52=32, so 32+52=90)
If two angles are supplementary and one of them is 52 degrees, what is the other one? Answer: 128 degrees (90-52=128, so 128+52=180)
Check your answers!
Quiz answers (out of 10 points):
Video series: https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-intro-euclid/v/geometric-precision-practice
Try this: https://mathigon.org/course/euclidean-geometry/introduction