Lesson 25 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 C B D ID: 725473
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Slide1
Addition & Subtraction Properties
Lesson 2.5Slide2
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
C
B
D
Yes
7 cm
7 cm
Yes
No
3 cmSlide3
If a segment is added to two congruent segments, the sums are congruent (Addition Property)
Theorem 8:
P
R
Q
S
Given: PQ
RS
Conclusion: 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.Slide4
If an angle is added to two congruent angles, the sums are congruent. (Addition Property)
Theorem 9:
Is
EFH necessarily congruent to
JFG?Slide5
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?Slide6
If congruent angles are added to congruent angles, the sums are congruent. (Addition Property)
Theorem 11:
Is
TWX necessarily congruent to TXW?Slide7
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?Slide8
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:Slide9
1.
NOP NPO
2. ROP RPO
3. NOR NPR
Given
Given
If angles are subtracted from angles, the differences are .
(Subtraction property)Slide10
HEF is supp. to
EHG.
GFE is supp. to
FGH.
EHF FGE
GHF HGE
EHG FGH
HEF GFE
Given
GivenGiven
GivenIf angles are added to angles, the sums are . (Addition Property)
Supplements of s are .