# 4.10 - Lines, Rays, and Angles

The student will

a) identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and vertices; and

b) identify representations of lines that illustrate intersection, parallelism, and perpendicularity.

### BIG IDEAS

• So that I can understand how angles, lines, points, rays, etc. play an important role in creating architecture.

• So that I can use angles, lines, points,and rays when describing geometric figures.

• Understanding lines, points, intersecting lines, parallelism, and perpendicularity helps us understand and describe different polygons.

### UNDERSTANDING THE STANDARD

• Points, lines, line segments, rays, and angles, including endpoints and vertices are fundamental components of noncircular geometric figures.
• A point is a location in space. It has no length, width, or height. A point is usually named with a capital letter.
• The shortest distance between two points in a plane, a flat surface, is a line segment.
• A line is a collection of points extending infinitely in both directions.  It has no endpoints. When a line is drawn, at least two points on it can be marked and given capital letter names. Arrows must be drawn to show that the line goes on in both directions infinitely (e.g., , read as “the line AB”).
• A line segment is part of a line. It has two endpoints and includes all the points between those endpoints. To name a line segment, name the endpoints (e.g., , read as “the line segment AB”).
• A ray is part of a line. It has one endpoint and extends infinitely in one direction. To name a ray, say the name of its endpoint first and then say the name of one other point on the ray (e.g., , read as “the ray AB”).
• An angle is formed by two rays that share a common endpoint called the vertex.  Angles are found wherever lines or line segments intersect.
• An angle can be named in three different ways by using:
• three letters in order: a point on one ray, the vertex, and a point on the other ray;
• one letter at the vertex; or
• a number written inside the rays of the angle.
• A vertex is the point at which two lines, line segments, or rays meet to form an angle.  In solid figures, a vertex is the point at which three or more edges meet.
• Lines in a plane either intersect or are parallel. Perpendicularity is a special case of intersection

• Intersecting lines have one point in common

• Students need experiences using geometric markings in figures to indicate congruence of sides and angles and to indicate parallel sides.

•  Parallel lines lie in the same plane and never intersect.  Parallel lines are always the same distance apart and do not share any points.  The symbol ∥ indicates that two or more lines are parallel.  For example, the notation is read as “line BC is parallel to line FG”.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Identify and describe points, lines, line segments, rays, and angles, including endpoints and vertices. (a)
• Use symbolic notation to name points, lines, line segments, rays, and angles. (a)
• Identify parallel, perpendicular, and intersecting line segments in plane and solid figures. (b)
• Identify practical situations that illustrate parallel, intersecting, and perpendicular lines. (b)
• Use symbolic notation to describe parallel lines and perpendicular lines. (b)

### KEY VOCABULARY

Updated: Aug 22, 2018