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.

Given: 3x+4=16

Prove: x=4

Now we'll add postulates, and use segments in addition to numbers and variables.

-Between any two points there can be only one line.

-The congruence of segments is reflexive, symmetric, and transitive.

Example:

Given: AB=BC , C is the midpoint of BD

Prove: AB=CD

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