Question

given that ef || hj and ef = hj, prove that △egf ≅ △jgh.
statement reason

1. ∠e = ∠j alternate - interior angle theorem
2. ef || hj given
3. ∠egf = ∠jgh vertical angle theorem
4. △egf ≅ △jgh aas
5. ∠e and ∠j are alternate - interior angles definition of alternate - interior angles
6. ∠egf and ∠jgh are vertical angles definition of vertical angles
7. ef = hj given

the proof shown is written in an incorrect order. what is a possible order that the statements and reasons could be written in?
7, 6, 1, 3, 5, 2, 4
two of these
7, 6, 3, 5, 2, 1, 4
2, 5, 6, 7, 1, 3, 4

Explanation:

Step1: Start with given

We start the proof by stating the given information. The given statements are "EF || HJ" and "EF = HJ", so we should start with the given "EF || HJ" which is statement 2.

Step2: Define vertical - angles

After stating the parallel - lines given, we can define vertical angles. Statement 5 and 6 are about the definition of vertical angles and should come next.

Step3: State other given

Then we state the other given "EF = HJ" which is statement 7.

Step4: Use angle - related theorem

After establishing the given and vertical - angle definitions, we use the Alternate Interior Angle Theorem to get ∠E=∠J (statement 1).

Step5: Use vertical - angle theorem

Then we use the Vertical Angle Theorem to get ∠EGF = ∠JGH (statement 3).

Step6: Prove congruence

Finally, with the established angles and side, we can prove that △EGF≅△JGH by AAS (statement 4).

Answer:

2, 5, 6, 7, 1, 3, 4