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?
5, 2, 1, 6, 3, 4, 7
two of these
6, 3, 5, 1, 2, 7, 4
6, 3, 7, 5, 2, 1, 4

Explanation:

Step1: Identify vertical - angles first

We start with identifying that ∠EGF and ∠JGH are vertical angles (Statement 6 and Reason: Definition of Vertical Angles). Then we state the Vertical - Angle Theorem (Statement 3).

Step2: Use given side - length

Next, we use the given fact that EF = HJ (Statement 7).

Step3: Use parallel - lines facts

Then we use the fact that EF || HJ (Statement 2). After that, we use the definition of alternate interior angles (Statement 5) and then the Alternate Interior Angle Theorem to get ∠E=∠J (Statement 1).

Step4: Prove congruence

Finally, we use the AAS (Angle - Angle - Side) criterion to prove that △EGF≅△JGH (Statement 4).

Answer:

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