Lesson 2.5Addition and Subtraction Properties

Objective:

After studying this lesson you will be able to apply the addition and subtraction properties of segments and angles.

A B C D7cm 7cm3cm

In the diagram above AB = CD. Do you think that AC = BD?

Suppose that BC were 5 cm. Would AC = BD?

Does the length of BC have any effect on whether AC = BD?

Theorem 8 If a segment is added to two congruent segments, the sums are congruent. (addition property of equality)

Given:

Prove:

PQ RS

P Q R S

PR QSStatements Reasons

1.

2. 2.

1.

3.

4.

3.

4.

PQ RS GivenPQ RS Def. of congruent segmentsPQ QR RS QR Addition Property of Equality

PR QS Substitution

5. 5.PR QS Def. of congruent segments

Theorem 9 If an angle is added to two congruent angles, the sums are congruent.(Addition Property of Equality)

Theorem 10 If congruent segments are added to congruent segments, the sums are congruent. (Addition Property of Equality)

Do you think that is necessarily congruent to ?

KMPO

P S O

K R M

Theorem 11 If congruent angles are added to congruent angles, the sums are congruent. (Addition Property of Equality)

W X

Y

T

Do you think that is necessarily congruent to ?

TWXTXW

Theorem 12 If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. (Subtraction property)

O

K

N

P

R

If KO = KP and NO = RP

Is KN = KR?

Given:

Conclusion:

NPONOP

ROP RPO

Statements Reasons

1.

2. 2.

1.

3. 3.

O

N

R

P

Theorem 13 If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. (Subtraction property)

NPRNOR

Statements Reasons

1.

2. 2.

1.

A

E

BF

D

Given:

Conclusion: ?

AB CD

C

Statements Reasons

1.

2. 2.

1.

3.

4.

3.

4.

5.

6.

5.

6.

Given:

Conclusion:

is supplementary to

is supplementary to

FGE

HGE

HEF EHG

GFE FGH

EHF

GHF

HEF GFE

H G

E F

Lesson 2.5 Worksheet

Homework

Summary…

How are the addition and subtraction theorems that you just learned similar/different?