This document contains notes from a geometry class on addition and subtraction properties of segments and angles. The class covered: [1] Using addition and subtraction properties as reasons in proofs and to find measures, [2] The addition and subtraction properties themselves for segments and angles, and [3] When to use addition vs subtraction in proofs. Examples were provided and homework assigned involving applying these properties.

1. Geom2­5hour3.notebook September 20, 2011
BELL WORK:
Find m UBF.
U
V
(x+46)0 (4x­2)0
B
A F
Agenda for the Day:
• questions
• 2.5 ­ Addition and Subtraction Properties
• exit slip
• work on homework
1

2. Geom2­5hour3.notebook September 20, 2011
After today's class, you should be able to:
1. Use addition and subtraction properties of segment
lengths and angle measures as reasons in proofs.
2. Use the same properties to find segment lengths
and angle measures.
2.5 Addition and Subtraction Properties
7 3 7
Ex: A B C D
Compare AB + BC and BC + CD
Ex: Q N C J
K A
Compare KA + AQ and NC + CJ
2

3. Geom2­5hour3.notebook September 20, 2011
Addition Property (segments): If a segment is added to 2
congruent segments, then the sums are congruent.
Addition Property REMIX (segments): If congruent segments
are added to congruent segments, the sums are congruent.
Compare 1 + 2 and 2 + 3
1
2
3
Addition Property (angles): If an angle is added to 2 congruent
angles, then the sums are congruent.
S W
G N
B Y
V T
Addition Property REMIX (angles): If congruent angles are added
to congruent angles, the sums are congruent.
3

4. Geom2­5hour3.notebook September 20, 2011
Compare
G H
EFH ­ GFH
E J and
GFJ ­ GFH
F
Subtraction Properties: If a segment (or angle) is subtracted from
congruent segments (or angles), then the differences are
congruent.
Compare RS + SB
and VP + PO
R
V
S P
B O
Subtraction Properties REMIX: If congruent segments (or angles)
are subtracted from congruent segments (or angles), the
differences are congruent.
When do you use the Addition Property vs. the Subtraction
Property in a proof?
• Use the Addition Property when the angles or segments are
bigger in the conclusion than in the given.
• Use the Subtraction Property when the angles or segments are
smaller in the conclusion than in the given.
4

5. Geom2­5hour3.notebook September 20, 2011
p.85 #2 M
Given:
Prove:
G H J K
p.85 #5
H G
Given:
Prove:
E F
5

6. Geom2­5hour3.notebook September 20, 2011
EXIT SLIP: p.86 #1
HOMEWORK: p.86 #2,3,6,8
due Thursday
not + or ­ property
6