Download 2.5 Justifying Statements and 2-Column Proofs

Geometry 1A
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2.5 Justifying Statements and 2-Column Proofs
Perpendicular Lines
Perpendicular lines are two lines that
intersect to form right angles. The symbol
for perpendicular to is .
Two-Column Proofs
A two-column proof organizes the statements and reasons used to justify the steps in
two columns with statements on the left and reasons (definitions, properties, postulates,
theorems) on the right.
Steps for Writing a Proof
1. Rewrite the given statement in statement one.
2. Mark the picture with the given information.
3. Look at one piece of given information:
a. What does it tell us?
b. What can we say?
c. Mark the picture with the new information
4. Look at the next piece of given information:
a. What does it tell us?
b. What can we say?
c. Mark the picture with the new information
Example 1: Use the figure to write the definition, property, postulate or theorem that
justifies each statement.
C
Given:
2 is supplementary to
BF bisects GBE
HD CF
CBE
1
E
a. CB BF
CF
c. m 2 m CBE
e.
180o
DBF is a right angle
B 6
D
b.
1
5
d.
2
3
f. m FBG m GBA
m FBA
2
3
F
5
A
H
4
G
Example 2: Write and justify two statements based on the information in the figure. Be
sure to use either definitions, properties, postulates, or theorems to justify your
statements.
C
Example 3: Complete the following proof.
A
B
D
P
Q
R
Given: Q is the midpoint of PR
QR RS
Prove: PR
S
RS
Statement s
Reasons
1. Q is the midpoint of PR
QR RS
2. PQ QR
1.
3. PR
3.
RS
2.
Example 4: Complete the proof.
1 and 2 are supplementary
m 1 68o
Prove: m 2 112o
Given:
1
Statement s
1.
1 and 2 are supplementary
m 1 68o
Reasons
1.
2.
2.
3.
3.
4.
4.
2
Example 5: Complete the proof.
Given: ABD and
Prove: x = 10
1.
Statements
ABD and DBC
are supplementary angles
Reasons
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
Example 6: Complete the proof.
Given: RQV and
Prove: x = 9
D
DBC are supplementary angles
o
(3x + 45)o (12x – 15)
B
A
R
S
Q
(4x + 30)o
(2x + 48)o
SQT are vertical angles
Statements
1. RQV and SQT
are vertical angles
2.
C
Reasons
1.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
V
T