Download 2-5 Postulates and Paragraph Proofs

2-5 Postulates and Paragraph
Proofs
Identify and use basic postulates
about points, lines and planes
Write Paragraph proofs
Postulate
• A statement that describes a fundamental
relationship between basic geometry
terms
• Postulates are accepted as true
Postulates
• 2.1 Through any 2 points, there is exactly
one line
• 2.2 Through any 3 points not on the same
line, there is exactly one plane
• 2.3 A line contains at least 2 points
• 2.4 A plane contains at least 3 points not
on the same line
• 2.5 If 2 points lie in a plane, then the
entire line containing those points lies
in the plane
• 2.6 If 2 lines intersect, then their
intersection is exactly 1 point
• 2.7 If 2 planes intersect, then their
intersection is a line
Determine whether each statement
is always, sometimes or never true
1. If a plane T contains line EF and EF
contains point G, then plane T contains
point G.
2. For Line XY, if X lies in plane Q and Y
lies in plane R, then plane Q intersects
plane R.
3. Line GH contains 3 noncollinear points.
Proofs
• Theorem – a statement or conjecture that
has been shown to be true.
• A proof is a logical argument in which each
statement you make is supported by a
statement that is accepted as true.
• In a paragraph (informal) proof you write a
paragraph to explain why a conjecture for
a given situation is true.
5 essential parts of a good proof
1. State the theorem or conjecture to be
proven.
2. List the given information.
3. If possible, draw a diagram to illustrate
the given information.
4. State what is to be proved.
5. Develop a system of deductive
reasoning.
At point C
Their intersection is exactly one point
Point D is on CD
collinear
A and D
Is a plane
collinear
Midpoint Theorem
• If M is the midpoint of line AB, then
line AM is congruent to line MB.
C
A
E
D
If E is the midpoint of AB and CD and AB=CD, prove
that AE = ED
midpoint
Since E is the ____________
of AB and CD, by the
___________________,
AE=EB and CE=ED. By the
Definition of midpoint
definition of congruent segments,
______________________________.
Since AB = CD,
AE = EB = ½ AB and CE = ED = ½ CD
________________
by the multiplication property. So
½ AB = ½ CD
AE = ED and by the definition of
______________________,
AE = ED
Congruent statements
B