Advanced Geometry Inductive Reasoning Lesson 1

Basic Geometric Figures

What is Geometry?

Geometry is a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids.

Undefined Terms

A

point

is a location in space. It has no size and no shape.

A

line

is made up of points. It has no thickness or width and extends infinitely in two directions.

A

plane

is a flat surface made up of points. It has no depth and extends infinitely in all directions.

R F

l

C X

P

G M

Naming Figures

Point

:

a CAPITAL letter

M

Line

:

• 2 points and a line symbol • a lowercase script letter

FR

line

l

Plane

:

• 3 noncollinear points • a CAPITAL script letter plane CXG plane P

Examples: Use the figure to name each of the following.

a point not contained on line

a

M

a line containing point K , , or

line a

a plane containing point L

Are points F, E, and D collinear?

NO. Point D is on a different line.

Collinear

Are points B, A, and D collinear?

YES

Are points C and G collinear?

YES. There is a line that contains points C and G.

Coplanar

Are points G, D, B, and E coplanar? Explain.

NO. Points G, D, and B all lie in plane GDB, but point E does not.

Examples: Use the figure to answer each question.

How many planes appear in this figure?

4

Name 3 points that are collinear.

C, G, and B

Name 4 points that are coplanar.

C, G, B, and A OR A, B, D, and E

Example: Draw and label a figure for each relationship.

Plane P contains lines m and n that intersect in R

Line Segments

Drawn as

:

a line with no arrowheads

B A

Named by

:

the 2 endpoints and a segment symbol

AB

Example: Draw and label a figure for each relationship.

Plane R at point P. Add point C on plane R so that it is not

Betweenness

If a point is between two other points on a line, addition or subtraction can be used to find a missing measure.

Example:

Find the measure of each segment.

Find LM.

Examples:

Find x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.

Congruent

Symbol

:



PS



QR

Red slashes on the figure also indicate that segments are congruent.

Midpoint Definition:

the point on a segment that divides the segment into two congruent segments

Bisector Definition:

any figure that divides another figure into two congruent parts