1. Geometry Introductory Terms

2. Point
An undefined term. A point has no length or width, it just determines a specific location.
Labels – a single capital letter, can be written out as you see below.
Point A A

3. Line
An undefined term. Usually defined as an unlimited collection of points in a straight row. A line extends forever in opposite directions.
Labels
Two letters with two points from the line, any order and double arrow above letters
The word line then two letters with no arrow above line HG
The word line with lower case italics letter from the end of the line line h
<
> h

4. Ray
A figure that begins at a certain point and extends forever in one direction only. The point where the ray begins is known as its endpoint. Order is very important when labeling a ray. Endpoint must come first then directional point.
Can also be written as the word ray then two letters contained on the ray. Endpoint must still come first.

5. Segment
Part or section of a line. It has two end points with a straight connection. Order is not important when labeling a segment.
Can also be written with the word segment and then the two endpoints from the segment. Order will not be important.

6. Collinear
Points that lie on the same line. Points P, Q, and R are collinear.

7. Non-Collinear
Points that do not lie on the same line. H is non-collinear with points A, B, and C.

8. Plane
An undefined term. A flat surface that extends infinitely in all directions. Three non-collinear points can also determine a plane. Order of the letters to label is not important.
Labels:
-the word plane with three random letters from the figure (plane ABD)
-Just three capital letters mushed together (DCB)
- the word plane with a single italic letter from the corner of the figure (plane R) R

9. CoPlanar
Elements that lie on the same plane. This includes points, segments, rays and lines.
Points A, B, and C are coplanar points. D is not.
Line AC is coplanar with ray BC. Ray AD is not.

10. Non-CoPlanar
Elements that do not lie on the same plane. This can be lines, segments, rays or points.
D is non-coplanar with plane ABC. All four points are not contained on the same plane.

11. Intersection
When lines, rays, segments or planes meet, they share something in common. This is called an intersection of elements. The intersection can be a point, ray, segment, or line.
Point of Intersection

12. Perpendicular Lines
Two lines in the same plane that intersect to form 90° angles.

13. Parallel Lines
Two lines in the same plane which never intersect. Figures are the same distance apart at any given set of points. Planes, segments, and rays can also be parallel. Points cannot be parallel.

14. Skew Line AD is skew with line BC.
Lines, rays, or segments that do not lie in the same plane, do not intersect and are not parallel. Planes and points cannot be skew.
Line AD is skew with
line BC.

15. Skew example
Find a segment skew to AB H A G E D B F C

16. Bisector
A point, line, segment, ray or plane that cuts an element into two congruent parts.
Red ray bisects the angle into two smaller angles of equal value.
Point M bisects segment AB into two smaller but equal segments.

17. Perpendicular Bisector
A segment, line, plane or ray that creates a right angle through a segment’s midpoint. The segment is the element bisected. Lines cannot be bisected since they have no endpoints neither can points, rays or planes.

18. Angle
An angle is formed by two rays which begin at the same point or the intersection of two lines, segments or planes.

19. Name parts of an angle
A C B

20. Naming an Angle
Many different names exist for the same angle. For the angle below, PBC, PBW, CBP, and WBA are all names for the same angle. Notice the vertex is always the middle letter.

21. Name an angle
A C A D 2
B B C

22. Measure an angle Use a protractor. Must label in degrees.
Put pivot (cross hairs) on the vertex.
Line up zero degree with one side of the angle.
Read measurement using other side of the angle.

23. Acute Angle
An ACUTE ANGLE is an angle whose measure is more than zero but less than 90º.

24. Right Angle
A RIGHT ANGLE is an angle whose measure is 90º.

25. Obtuse Angle
A OBTUSE ANGLE is an angle whose measure is more than 90° but less than 180°.

26. Straight Angle
A STRAIGHT ANGLE is an angle whose measure is 180°. These are opposite rays which makes a line.

27. Points Interior, Exterior, On
Interior = inside the angle
Exterior = outside the angle
On = part of the sides of the angle or the vertex

28. Example
KF is a bisector of angle HKI. Angle HKF is 5x. Angle FKI is 4x + 9. Solve for x.

29. Example
KF is a bisector of angle HKI. Angle HKI is 8s Angle FKI is 2(s+11). Solve for x.

30. Adjacent Angle
ADJACENT ANGLES are angles in the same plane, that have a common vertex and a common side, but no common interior points. Nothing overlaps.

31. Adjacent Example
I lies in the interior of KJH. If HJI=9x and KJI=3x + 6, find x so that KJ  JH.

32. Linear Pair adjacent angles whose non common sides are opposite rays.
These are two angles that are connected that make a line.

33. Linear Pair Example Name a linear pair of angles
from the drawing shown. C D B P E A

34. Vertical Angles
Two nonadjacent angles formed by two intersecting lines or segments.
Vertical angles will always have the same measure.

35. Vertical Angle Example
Find the value of x.
4x
36

36. Complementary Angles
If the sum of the measures of two angles is 90 degrees, then the angles are COMPLEMENTARY.
The angles do not need to be adjacent but they can be adjacent.

37. Complementary Example
The measures of BGC and CGD are complementary. If BGC = 16x – 4 and CGD = 2x + 13, find x and CGD.

38. Supplementary Angles
If the sum of the measures of two angles is 180 degrees, then the angles are SUPPLEMENTARY.
A linear pair is supplementary but supplementary angles do not have to be touching.

39. Supplement Example
The measure of an angle’s supplement is 44 less than the measure of the angle. Find the measure of the angle and its supplement.

40. Resources Photos, diagrams, animations and information collected at: