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Segment congruence theorem. Segment congruence is an equivalence relation. In other words, if PQ, RS and UV are segments then: 1. PQ = PQ (Reflexivity) 2. If PQ = RS then RS = PQ (Symmetry) 3. If PQ = RS and RS = UV then PQ = UV (Transitivity) In layman's terms, a symbol or relation that satisfies Reflexivity, Symmetry and Transitivity can more or less be treated as an equals sign. Proof: 1. Note that d(P,Q)=d(P,Q). By definition, PQ = PQ. 2. If PQ = RS then by definition, d(P,Q)=d(R,S). So, d(R,S)=d(P,Q) and by definition, RS = PQ. 3. ?

Segment congruence theorem. Segment congruence is an equivalence relation. In other words, if PQ, RS and UV are segments then: 1. PQ = PQ (Reflexivity) 2. If PQ = RS then RS = PQ (Symmetry) 3. If PQ = RS and RS = UV then PQ = UV (Transitivity) In layman's terms, a symbol or relation that satisfies Reflexivity, Symmetry and Transitivity can more or less be treated as an equals sign. Proof: 1. Note that d(P,Q)=d(P,Q). By definition, PQ = PQ. 2. If PQ = RS then by definition, d(P,Q)=d(R,S). So, d(R,S)=d(P,Q) and by definition, RS = PQ. 3. ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Segment congruence theorem. Segment congruence is an equivalence relation. In other words, if PQ, RS and UV are segments then: 1. PQ = PQ (Reflexivity) 2. If PQ = RS then RS = PQ (Symmetry) 3. If PQ = RS and RS = UV then PQ = UV (Transitivity) In layman's terms, a symbol or relation that satisfies Reflexivity, Symmetry and Transitivity can more or less be treated as an equals sign. Proof: 1. Note that d(P,Q)=d(P,Q). By definition, PQ = PQ. 2. If PQ = RS then by definition, d(P,Q)=d(R,S). So, d(R,S)=Dd(P,Q) and by definition, RS = PQ. 3. ? Question: Complete the proof of segment congruence theorem.
Transcribed Image Text:Segment congruence theorem. Segment congruence is an equivalence relation. In other words, if PQ, RS and UV are segments then: 1. PQ = PQ (Reflexivity) 2. If PQ = RS then RS = PQ (Symmetry) 3. If PQ = RS and RS = UV then PQ = UV (Transitivity) In layman's terms, a symbol or relation that satisfies Reflexivity, Symmetry and Transitivity can more or less be treated as an equals sign. Proof: 1. Note that d(P,Q)=d(P,Q). By definition, PQ = PQ. 2. If PQ = RS then by definition, d(P,Q)=d(R,S). So, d(R,S)=Dd(P,Q) and by definition, RS = PQ. 3. ? Question: Complete the proof of segment congruence theorem.
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