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1. Foundations of Geometry
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Geometry

1.03 Introduction to geometric notation

Lesson
Practice
Adaptive
Worksheet
What do you remember?
1

Complete the definition using one of the given terms, then draw an example.

i
Point
ii
Line
iii
Plane
iv
Line segment
v
Ray
vi
Angle
vii
Collinear
viii
Plane figure
a
A ⬚ has one endpoint and extends without end in one direction.
b
A ⬚ has two dimensions extending without end. It is often represented by a parallelogram.
c
A ⬚ has no dimension. It is a location on a plane. It is represented by a dot.
d
An ⬚ is formed wherever two lines, segments or rays intersect. The point of intersection is called the vertex of the ⬚.
e
A ⬚ consists of two endpoints and all the points between them.
f
A ⬚ has one dimension. It is an infinite set of points represented by a ⬚ with two arrowheads that extend without end.
2

Using proper notation, identify the following features of the diagram shown:

a

A line segment with one endpoint at point D

b

A set of three collinear points

c

A line passing through point F

d

A ray starting from point A

e

Another name for \overrightarrow{BE}

Rays, lines, points and segments are drawn intersecting each other. Speak to your teacher for further description of the image.
3

Using proper notation, identify the following features of the diagram shown:

a

A line that is contained in plane PQR

b

A line that intersects, but is not contained in, plane PQR

c

Four coplanar points

d

Three collinear points

e

An angle that is contained in the plane

f

An angle that is not contained in the plane

g

A pair of opposite rays

A plane containing non-collinear points P, Q, R and S. Line A Q and line B R intersect the plane at points Q and R and meet at point C. Auxillary rays are drawn for ray Q C and ray R C.
4

Name the geometric figure shown in two different ways.

A parallelogram is drawn with a letter R in the upper right hand corner. Letters X, Y and Z are arranged inside the quiadrilateral in triangular position with a dark dot beside each letter.
5

State the intersection of the two geometric figures shown in each of the following diagrams:

a

\overleftrightarrow{AB} and \overleftrightarrow{BC}

A line with arrow heads pointing in opposite directions is drawn with 2 dots labeled B and C. Another line with two arrowheads pointing in opposite direction intersect the first line. It has 2 dots labeled A and B.
b

\overleftrightarrow{AB} and Plane BCD

Plane with three non collinear points B C D. Line A B intersect the plane at a point. Ray B A is drawn diagonally upward. A ray starting from B is an auxillary ray opposite the direction of ray B A.
c

\overleftrightarrow{XZ} and Plane XYZ

Plane containing non collinear points X Y Z. Line X Z lies on the plane.
d

Planes PQR and QRS

A plane containing points P Q R intersect a plane containing Q R S.
6

The given figure is a cube. Identify three pairs of skew lines.

The image shows a geometric diagram of a cube. Each vertex of the cube is labeled: A is at the front lower-left, B is at the front lower-right, C is at the front upper-left, and D is at the front upper-right. The rear vertices are labeled correspondingly with E at the lower-right, F at the lower-left, and G at the upper-left. Diagonal lines are drawn inside the cube connecting opposite vertices: A to B, G to E, C to D, and E to F. Ask your teacher for more information.
Let's practice
7

Answer the following questions:

a

Draw a ray that has point A as an endpoint.

b

Write a name for the ray you have drawn.

c

State how many points you needed to use to name the ray.

d

When naming the ray, determine whether the order of the points matters. Explain your answer.

8

\overleftrightarrow{PQ} and \overleftrightarrow{RS} meet at point M.

a

Draw a diagram that shows this.

b

Identify a pair of opposite rays in the diagram.

9

Planes DEF and EFG have common points of E and F.

a

Draw a diagram that shows this.

b

Name the full intersection of the two planes.

10

Draw a diagram that shows \overline{AB} contained in plane P, with \overleftrightarrow{CB} intersecting (but not contained in) the plane.

Let's extend our thinking
11

Determine whether each statement is true or false. If true, draw an example. If false, draw a diagram that shows it is false.

a

Through any two points, there is exactly one line.

b

Two distinct pairs of points always form two different lines.

c

If two points are both contained in a plane, then the line that they form is also entirely contained in that plane.

d

For any three collinear points, there is exactly one plane that contains them.

e

If three points are collinear, they cannot be contained in a single plane.

f

For any two distinct lines, there is a plane which contains them both.

12

For each geometric figure, determine a real life example which is a model for the figure. State whether there any limitations or restrictions on the real life example.

a

A ray

b

A line

c

A plane

13

Explain the similarities and differences between:

a
A line segment and a ray.
b
A line and a ray.
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