Section 3 - Proofs Involving Segments
A proof is a series of logical statements, each statement helping to prove an idea, and each statement being backed by a theorem or postulate. A postulate is a rule that is widely accepted throughout the world. Most proofs are written in two columns, these proofs are called two-column proofs. A proof always starts with a given, which is something taken for granted. It then asks you to prove something using the given and the theorems you already know. Let's try a proof with theorems we already know.
Now we'll add postulates, and use segments in addition to numbers and variables.
-Segment Addition Postulate: AB+BC=AC
-Between any two points there can be only one line.
-The congruence of segments is reflexive, symmetric, and transitive.
Given: AB=BC , C is the midpoint of BD
Practice these proofs.
1) Given: LE = MR and EG = RA , Prove: LG = MA
2) Given: AB = BC and BC = CD , Prove: AB = CD
3) Given: QR = RS , Prove: QS = 2RS
4) Given: AC = AD and AB = AE , Prove: BC = ED
5) Given: Segment ABCD , Prove: AD = AB + BC + CD
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