1.03 Mathematical Language

	Blueprints for this Lesson:
	Identify and define a segment, a ray, a vertex, and an angle. Practice naming and reading mathematical terms and symbols.

Foundational Knowledge:

Name the plane that represents the top of this box.
Name the point that is at the intersection of the top, front, and right sides of the box.

Check Your Answers

A box is drawn with 8 vertex points labeled. The top of the box has vertex points F G C and B. These points are written in clockwise order starting with the upper left corner of the box. The bottom of the box has vertex points E H D A. These points are written in clockwise order starting with the back left point on the base of the box.

Framework for Understanding:

Math language is extremely precise. Geometry is known for its specific use of letters and symbols. Understanding the material in a lesson is often a matter of recognizing the "name" of a figure. For your answers to be understood both by your instructor and others, you must use accepted symbols.

Printed Capital Letters

A printed capital letter is used to name a point. The name may refer to a point by itself in space; however, it is often a point on a line. A printed capital letter may reference the endpoint of a segment or ray. A printed capital letter could also draw your attention to the vertex of an angle or a polygon. Printed capital letters are also used to name points on a number line or points on a coordinate plane.

Take a look at the illustrations below to see the ways that printed capital letters can be used.

the illustrations of how printed capital letters can be used

Text-only version

Cursive Capital Letters

A cursive capital letter is used to name a plane. Two illustrations are shown below.

Cursive capital letter R is naming a plane. Cursive capital letters M, C and S name three planes which make up three sides of a box

Cursive Lowercase Letters

Lines can be named using any two points on the line or using a single cursive lowercase letter. See the illustrations below.

A line is drawn and labeled with a cursive lowercase l. Three lines are drawn so that two are parallel to each other and the third one crosses the other two. The parallel lines are named using lowercase cursive x and y. The third line is named lowercase cursive m.

Printed Lowercase Letters

Printed lowercase letters are used to identify unknown lengths in a diagram or illustration. For polygons, the lowercase letter usually matches the capital letter used to name the vertex opposite that side. Lowercase letters may also be used for unknown angle measures.

Segment A B is drawn with the measurement labeled x. Triangle M N O is drawn with the missing sides labeled m, n and o. M is opposite side m. N is opposite side n. O is opposite side o. The unknown angle formed at vertex point O is labeled x.

Often angle measures are more likely to be tagged with numbers or Greek letters.

A triangle is drawn with a missing angle measure labeled using the greek letter theta. Two lines are drawn so that they intersect. The intersection creates 4 angles labeled 1, 2, 3 and 4.

A Special Printed Lowercase Letter: m

The letter m is used to indicate the measure of an angle or arc.

Two-letter Sequence

Two capital letters printed together can mean one of the following things:

Two letters are used to represent the name of a line. The notation for the line shown below is or .
Two letters are used to represent the name of a ray. The notation for the ray shown below is .
Two letters are used to represent the name of a segment. The notation for the segment shown below is or .
Two letters are used to represent the length of a line segment. The notation for the length of the segment shown below is AB. In this case AB = 7.

Three-letter Sequence

Three capital letters printed together can be used to name one of the following:

Three letters are used to represent an angle. The notation for the angle shown below is or .
Three letters are used to represent a triangle. The notation for the triangle shown below is .
Three letters are used to represent a major arc. The notation for the major arc shown below is .
Three letters are used to represent a plane. The notation for the plane shown below is plane ABC.

Click here to see a printable list of Geometry symbols.

The walls and ceiling of a room consist of congruent square tiles. The room is in the shape of a rectangle.

Look at the picture of the ceiling above. Do you see any Geometric shapes? Some of the items you might think of can be described as undefined terms, definitions, postulates, or theorems. In addition, it is very important to utilize appropriate mathematic symbolism when writing. Think about the following questions describing the picture above.

What undefined term describes where the bottom, back and left planes meet?
Describe a line you see above.
The intersection of two planes form what shape?
Two lines intersect at what shape?
Points that lie on the same line are called what kind of points?

Check Your Answers

Considering the picture below, write a paragraph that describes what you see. Include at least six Geometric terms you have learned from this lesson. You will be submitting your paragraph as part of the assessment for lesson 1.03.

Hallway drawn in perspective view. Round lights are recessed in the ceiling. Many doorways appear on both the left and right walls.

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