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Organizing a Proof
4-2C
How do you write out a proof?
What are the three methods that
can be used to write a proof?
What is a proof?
The employee at Best Buy asked for
proof of the purchase.
The detective found fingerprint proof
to use in the robbery case.
A Proof—a sequence of true facts
(statements) placed in a logical
order.
How do we convince others
that a proof is valid (true)?
We supply a reason to justify each
statement. Those reasons include:
The hypothesis (Given)
Information that can be assumed from a
figure
Definitions
Postulates and algebra properties
Theorems that have already been
proved.
If AC and BD bisect each
other at M, then AMB  CMD
Given: AC and BD bisect each other at M
Prove: AMB  CMD
A
B
Statements
1. AC AND BD bisect each
D
M
Reasons
1. Given
other at M
2. AM  MC , BM  MD
2. Def of bisect
3. AMB  DMC
3. Vertical angles cong.
4. AMB  CMD
4. SAS Postulate
C
Formats for Deductive Proofs
• Two column **
Statements and reasons columns (p.268)
• Paragraph
Uses plan and proof paragraphs (p. 267)
• Flow chart
Statements and reasons are given in
boxes and linked by arrows. (p. 268)
Convince Me!
Given: 1  4,
B
E
AC  CD,
5  6
Prove: ABC  DEC
Statements
1.1  4, AC  CD, 5  6
2.1& 2 form linear pair
1 2
5
6
C
A
3 4
D
Reasons
1.Given
2.Def linear pair
3 & 4 form linear pair
3.1supp. to2, 3 supp. to4 3.Supp cong angles cong
4.ABC  DEC
4.ASA
Complete the Proof
Given: X is the midpoint of VZ
1  2
Prove: VXW  ZXY
W
Z
1 X
2
V
Y
Statements
Reasons a. Supp of cong
1.X is the midpt of VZ
b
1. ___
2.VX  XZ
3. WXV  YXZ
d
2. ___
4. 1  2
5. VXW  ZXY
b
4. ___
e
3. ___
c
5. ___
angles cong
b. Given
c. SAA
d. Def of midpt
e. Vert angles cong
f. Rt angles cong
• How do you write out a proof?
Use two columns with one for
Statements and the other for
Reasons
• What are the three methods that can
be used to write a proof?
Two column
Paragraph
Flow chart
Assignment
Page 270, 1-2, 4-5, 11-13, 15-16