I’m literally desperate can someone help me figure this out

9514 1404 393

Explanation:

(In order avoid issues with the censor, we're going to rename point F as point G in this answer. Wherever you see G, you can use F in your own response to this question.)

General Approach

The perpendicular lines tell you these are right triangles. There are a few ways to show right triangles are congruent, one of which is the "HL theorem." It requires you show the hypotenuse and one leg are congruent in the two triangles.

Here, the hypotenuses, DE and AG, are shown as congruent. All that remains is to show one leg is congruent. We have no information about legs BE and CG, but we do have information that will let us show legs AC and DB are congruent.

Proof

1. DE ≅ AG, DC ≅ AB, GC⊥AC, EB⊥DB . . . . given

2. m∠EBD = 90°, m∠GCA = 90° . . . . definition of perpendicular lines

3. CD + CB = DB . . . . segment sum theorem

4. AB + CB = DB . . . . substitution property of equality (CD→AB)

5. AB +CB = AC . . . . segment sum theorem

6. DB = AC . . . . transitive property of equality

7. ΔACG ≅ ΔDBE . . . . HL theorem