Prove: AC=PR - A Challenge to Solve

[roshamboe]

proof!

god do i hate these things, ok here we go,
A------------B------------------------C
P------------Q------------------------R
Given:ABC, PQR, AB=PQ, BC=QR
Prove:AC=PR

The Attempt at a Solution

statements/Reasons
1.ABC and PQR/Given
2.AB=PQ and BC=QR/Given
3.AB+BC=PQ+QR/All lines are congruent so when added the sum is congruent
4.AB+QR=PQ+BC/Partition Postulate
5.AC=PR/When all of the parts of thine are congruent, the lines are congruent

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i'm pretty sure that's not right, can someone tell me where i went wrong?

 

[BigJDubs]

You have almost got it right, but you need to make a few changes. Statements/Reasons1. ABC and PQR/Given2. AB=PQ and BC=QR/Given3. AB+BC=PQ+QR/Transitive Property4. AC=AB+BC/Definition of Addition5. AC=PQ+QR/Substitution of Step 26. AC=PR/Transitive Property

 

[thomate1]

First of all, it's important to define your terms. In this proof, it seems like A, B, C, P, Q, and R are all points on a line, and AB, BC, PQ, and QR are line segments. It would be helpful to state this explicitly in your proof.

Secondly, it's important to state what you are trying to prove. In this case, you want to prove that AC is congruent to PR. This means that you need to show that the length of AC is equal to the length of PR.

Now, let's look at your proof:

1. ABC and PQR/Given
2. AB=PQ and BC=QR/Given
3. AB+BC=PQ+QR/All lines are congruent so when added the sum is congruent
4. AB+QR=PQ+BC/Partition Postulate
5. AC=PR/When all of the parts of thine are congruent, the lines are congruent

There are a few issues with this proof:

1. In step 3, you say that "all lines are congruent so when added the sum is congruent." This is not necessarily true. The fact that AB is congruent to PQ and BC is congruent to QR does not necessarily mean that AB+BC is congruent to PQ+QR. In order to prove this, you would need to use the Segment Addition Postulate, which states that if A, B, and C are collinear points, then AB+BC=AC.

2. In step 4, you use the Partition Postulate, which states that if a line is divided into two parts, then the sum of the lengths of the parts is equal to the length of the whole line. However, you haven't actually divided the line into two parts in your diagram. Instead, you have two separate lines (AB and BC) and two separate lines (PQ and QR). You can't use the Partition Postulate in this case.

3. In step 5, you say that "when all of the parts of thine are congruent, the lines are congruent." This is not a valid reason. In order to prove that AC is congruent to PR, you need to show that the length of AC is equal to the length of PR. Simply stating that "all of the parts are congruent" is not enough to prove this.

Here is a