Question

eg ≅ fh. complete the proof that △egh ≅ △fhg.

statement
1
2 ∠efh ≅ ∠feg
3 eg ≅ fh
4 ∠feg ≅ ∠egh
5 ∠fhg ≅ ∠efh
6 ∠efh ≅ ∠egh
7 ∠fhg ≅ ∠egh
8 gh ≅ gh
9 △egh ≅ △fhg

reason
given
given
given
alternate interior angles theorem
alternate interior angles theorem
transitive property of congruence

reflexive property of congruence
sas

Explanation:

Step1: Use Transitive Property of Congruence

Since \(\angle EFH\cong\angle FEG\) (Given) and \(\angle FEG\cong\angle EGH\) (Alternate Interior Angles Theorem), by the Transitive Property of Congruence, \(\angle EFH\cong\angle EGH\).

Step2: Use Transitive Property of Congruence again

Given \(\angle EFH\cong\angle FHG\) (Alternate Interior Angles Theorem) and \(\angle EFH\cong\angle EGH\) (from Step 1), then \(\angle FHG\cong\angle EGH\) by the Transitive Property of Congruence.

Answer:

Transitive Property of Congruence