Warm‐Up:
* Is "is parallel to" an equivalence relation for a set of lines?
Explain
* Is " is the bisector of" an equivalence relation for the set of line segments?
Exaplain
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3.9 Postulates Concerning Addition and Subtraction The Partition Postulate: A whole is equal to the sum of all its parts.
‐ this postulate applies to segments or to their lengths
‐this postulate also applies to angles or their measures
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The Addition Postulate: *If a=b, and c=d, then a+c = b+d
*If equal quantities are added to equal quantities, the sums are equal
*If congruent segments are added to congruent segments, the sums are congruent
*If congruent angles are added to congruent angles, the sums are congruent
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Ex) Given: ABC and DEF with AB=DE and BC=EF
Prove: AC=DF
Statements
Reasons
*If equal quantities are added to equal quantities, the sums are equal
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*If congruent segments are added to congruent segments, the sums are congruent
Given: ABC and DEF with AB DE and BC EF
Prove: AC DF
*If congruent angles are added to congruent angles, the sums are congruent (Same style proof!)
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The Subtraction Postulate: *If a=b, and c=d, then a‐c = b‐d
*If equal quantities are subtracted from equal quantities, the differences are equal
*If congruent segments are subtracted from congruent segments, the differences are congruent
*If congruent angles are subtracted to congruent angles, the differences are congruent
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Given: ABG ≅ DEH
GBC ≅ HEF
Prove: ABC ≅ DEF
Statements
Reasons
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Given: m DAC = m ECA
m 1 = m 2
Prove: m 3 = m 4
Statements:
Reasons:
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Given: AB ≅ AC
DB ≅ EC
Prove: AD ≅ AE
Statements:
Reasons:
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Homework:pg 121 #1,2,5,7,9,10
Honors: pg 121 #1,2,4,5,7,9,10,11
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