Page 188 - Math Course 2 (Book 2)

Postulates and Paragraph Proofs
Mo. 12

Lesson 5
Let’s Begin

KEY CONCEPTS:
Points and Lines
1. Identify and use basic postulates about
points, lines, and planes.
2. Write paragraph proofs. Example

SNOW CRYSTALS

MO. 12 - L5a Some snow crystals are shaped like regular
hexagons. How many lines must be drawn to
Identify and Use Basic interconnect all vertices of a hexagonal snow
Postulates crystal?

Explore The snow crystal has six vertices since
a regular hexagon has six vertices.
Vocabulary A-Z Plan Draw a diagram of a hexagon to

Let us learn some vocabulary illustrate the solution.
A B
postulate
is a statement that is accepted as true.

axiom F C
is a statement that is accepted as true.

Through any two points, there is exactly one
line.

Through any three points not on the same E D
line, there is exactly one plane. Solve
Label the vertices of the hexagon A, B, C, D, E, and
POSTULATES F. Connect each point with every other point. Then,
count the number of segments. Between every
two points there is exactly one segment. Be sure
12.1 Through any two points, there is exactly one to include the sides of the hexagon. For the six
line. points, fifteen segments can be drawn.

Examine
12.2 Through any three points not on the same In the figure, AB, BC, CD, DE, EF, AF, AC, AD, AE, BD,
line, there is exactly one plane BE, BF, CF, CE, and DF are all segments that

12.3 A line contains at least two points. connect the vertices of the snow crystal.
12.4 A plane contains at least three points not on
the same line.
Answer 15
12.5 If two points lie in a line, then the entire line
containing those points lies in that plane.

12.6 If two lines intersect, then their intersection
is exactly one point.

12.7 If two plane intersect, then their intersection
is a line.

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