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U3 L5 Proofs with Partitioning Lesson.notebook
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Nov 1211:36 AM
Unit 3 Lesson 5
Proofs with Partitioning
Objective: Students will use adding and subtracting in order to establish equality.
Nov 1211:41 AM
Unit 3 Lesson 5
Proofs with PartitioningSince geometry proofs involve reasoning about spatial relationships, we often need to add and subtract measures of segments and angles in order to establish equality (and thus congruence). We do this using the axioms of equality that we saw in an earlier lesson.
Statements Reasons
U3 L5 Proofs with Partitioning Lesson.notebook
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Nov 1211:44 AM
Statements Reasons
Sep 2912:52 PM
used in proofs
used in proofs
used in proofs
We just proved the congruence complements Theorem in excercise 2! Remember, once a theorem is proved, it is yours to keep.....meaning, you can simply use the theorem in a proof instead of going through all of the steps required in proving the theorem.
In an if...then statement,
the "if" is the given information
the "then" is what you have to prove.
U3 L5 Proofs with Partitioning Lesson.notebook
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Dec 67:35 AM
used in proofs
Let's prove this!
1
2
3
Given: <1 is supplementary to <3
<2 is supplementary to <3
Prove: <1 <2
Statements Reasons
<2 is supplementary to <3 <1 is supplementary to <3
1) 1) Given
2) 2) Supplementary angles sum to 1800
Linear Pair Postulate
U3 L5 Proofs with Partitioning Lesson.notebook
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Nov 1211:44 AM
In general, we refer to breaking a segment or angle into its component parts or building a segment or angle from its component parts as partitioning. Partitioning within a larger proof is common, but can be quite challenging.
Statements Reasons
Nov 1211:51 AM
Statements Reasons
U3 L5 Proofs with Partitioning Lesson.notebook
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Nov 1211:42 AM
Homework
U3 L5 Homework Section
Statements Reasons1)1) Given
2) CE = DE 2) A midpoint cuts a segment into 2 = parts
3)AC+CE = BD+DE 3) Addition Property
4) AE = AC+ CE
BE = BD + DE
4) Whole = sum of the parts
AE = BE5)
5) Substitutionor
6) E is the midpoint of AB
6) When a segment is divided into 2 = parts, then E is the midpoint
U3 L5 Proofs with Partitioning Lesson.notebook
6Nov 121:58 PM
From HW page
1) HD=JD, HC=JB
2) HD + DC = HC
JD + DB = JB
3) HD + DC = JD + DB
4) DC = DB
5) <1 = <2
6) ΔHDB ΔJDC
7) HB = JC
1) given
2) a whole is the sum of
it's parts
3) substitution
4) subtraction axiom
5) vertical angles are congruent
6) SAS theorem
7) CPCTC
Statement Reason
U3 L5 Proofs with Partitioning Lesson.notebook
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Nov 1410:17 AM
From HW page
1) m<1 = m<2, QN=RN,
SN MP, MN = PN
2) <MNS and < PNS are
right angles
3) <MNS=<RNS=90
4) m<1 + m<3=90
m<2 + m<4=90
5) m<1 + m<3=m<2 + m<4
6) m<3=m<4
7) MQN = PRN
8) QM=RP
1) given
2) perp. lines form
right angles
3) right angles are 90
4) a whole is the sum
of it's parts
5) substitution
6) subtraction axiom
7) SAS Theorem
8)CPCTC
Statement Reason
Statements Reasons
1) m 1 = m 2,
TMPSN MN=PN,QN=RN 1) Given
2) SNM & SNP are right
2) Perpendicular lines form right angles
3) SNM = 90o, SNP = 90o 3) All right angles = 90o
4) 3 complement 1
4 complement 2
4) If 2 angles sum to 90o, the are complementary
5) 3 45) Complements of = s are =
6) ΔMQN ΔPRN6) SAS
7) QM = RP7) CPCTC
U3 L5 Proofs with Partitioning Lesson.notebook
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Statements Reasons
1) AB AC, AD AE,
DC EB
1) Given
2) BC CB
3) AB = AD+ DB
AC = AE + EC
2) Reflexive Prop
3) Whole = the sum of its parts
4) substitution 4) AD + DB = AE + EC
5) BD = CE 5) Subtraction
6) ΔDBC ΔECB6) SSS
7) 7)
1 2CPCTC
U3 L5 Proofs with Partitioning Lesson.notebook
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