Question

The lengths C ⁢ E = C ⁢ D + D ⁢ E and D ⁢ F = E ⁢ F + D ⁢ E by segment addition. It was given that C ⁢ D = E ⁢ F and applying the substitution property of equality gives D ⁢ F = C ⁢ D + D ⁢ E . Since both C ⁢ E and D ⁢ F equal the same quantity, C ⁢ E = D ⁢ F by the transitive property of equality. It was also given that A ⁢ B = C ⁢ E . Applying the transitive property of equality again, A ⁢ B = D ⁢ F . Use the paragraph proof to complete the two-column proof. What statement and reason belong in line 4?

Answer 1

4. CE = DF

4. Given

Explanation:

Proofs are written ways to prove some property in math.

Completing the Proof

To complete the proof we need to look at what was given and what the next steps are. In the last step, DF takes the place of CE through the substitution property of equality. The only way that this can happen is if CE equals DF, then we can replace CE with DF in any equation. So, before we can replace CE, we need to state that CE = DF. This statement is given to us by the problem; thus, the reason for this statement is "given".

Transitive Property of Equality

The proof asks us to prove the transitive property of equality (PoE). The transitive PoE is often written as:

• If A=B and B=C, then A=C

The transitive PoE is extremely helpful in geometry when trying to prove equality or congruency between 2 angles, lines, or figures. The transitive property can also be used in proofs for other properties.