Question

Match the proof. I need help please​

Answer 1

Answer:

D, E, F, B, C, A, G

Step-by-step explanation:

D is the midpoint of AB, E is the midpoint of BC and DB || FC

This is given information from the diagram and statement.

∠B ≅ ∠FCE

Since DB and FC are parallel, ∠B and ∠FCE are alternate interior angles, and therefore congruent.

∠BED ≅ ∠CEF

∠BED and ∠CEF are vertical angles, and therefore congruent.

ΔBED ≅ ΔCEF

By angle-side-angle, these triangles are congruent.

DE ≅ FE, DB ≅ FC

Corresponding parts of congruent triangles are congruent.

AD ≅ DB, DB ≅ FC, therefore AD ≅ FC

From transitive property of congruence.

ADFC is a parallelogram

Since AD and FC are congruent and parallel, ADFC is a parallelogram.

DE is parallel to AC

Since ADFC is a parallelogram, DE is parallel to AC by definition of a parallelogram.