Addition & Subtraction Properties

Lesson 2.5

In the diagram above, AB = CD.

Do you think that AC = BD?

Suppose that BC were 3cm. Would AC = BD?

If AB = CD, does the length of BC have any effect on whether AC = BD?

A CB D

Yes

7 cm 7 cm

Yes

No

3 cm

If a segment is added to two congruent segments, the sums are congruent (Addition Property)

Theorem 8:

P RQ S

Given: PQ RSConclusion: PR QS

Proof: PQ RS, so by definition of congruent segments, PQ = RS. Now, the Addition Property of Equality says that we may add QR to both sides, so PQ + QR = RS + QR. Substituting, we get PQ = QS. Therefore, PR QS by the definition of congruent segments.

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

Theorem 9:

Is EFH necessarily congruent to JFG?

If congruent segments are added to congruent segments, the sums are congruent. (Addition Property)

Theorem 10:

Do you think that KM is necessarily congruent to PO?

If congruent angles are added to congruent angles, the sums are congruent. (Addition Property)

Theorem 11:

Is TWX necessarily congruent to TXW?

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

Theorem 12:

If KO = KP and NO = RP, is KN = KR?

If congruent segments (or angles) are subtracted from congruent segments (or angles) the differences are congruent. (Subtraction Property)

The only difference between Theorem 12 and 13 is that this one is plural.

Theorem 13:

1. NOP NPO2. ROP RPO3. NOR NPR

1.Given2.Given3.If angles are

subtracted from angles, the differences are . (Subtraction property)

1. HEF is supp. to EHG.2. GFE is supp. to FGH.3. EHF FGE4. GHF HGE5. EHG FGH

6. HEF GFE

1. Given2. Given3. Given4. Given5. If angles are added to

angles, the sums are . (Addition Property)

6. Supplements of s are .