Question

after proving a triangle congruent, what reason can you use to prove parts are congruent?
given eg || df, eg = df
prove: ed || gf
proof:

1. eg = df
2. given
3. eg || df
4. given
5. ∠egd ≅ ∠fdg
6. alt. int. ∠ thm.
7. gd ≅ gd
8. reflex. prop. of ≅
9. △egd ≅ △fdg
10. sas steps 1, 3, and 4
11. ∠edg = ∠fgd

6.

Explanation:

Step1: Recall the concept of CPCTC

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is a principle used to prove that parts of congruent triangles are congruent. After proving two triangles are congruent (in this case, \(\triangle EGD\cong\triangle FDG\) by SAS as per the proof steps: \(EG = DF\) (given), \(\angle EGD=\angle FDG\) (from step 3, \(EG\parallel DF\) and alternate - interior angles theorem), \(GD = GD\) (reflexive property)), we can use CPCTC to show that other corresponding parts (like \(\angle EDG=\angle FGD\)) are congruent.

Answer:

CPCTC