Mathematics, 08.08.2019 19:20, mykiagamble

Me to match this proof this is very difficult for me

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answered: lovwhydontwe

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D and E are midpoints; DB ║ FC

F. Given — That D and E are midpoints of segments AB and BC is in the Given statement at the beginning of the problem. That FC is parallel to DB is not stated or shown, but we can define it to be the case. (There would need to be direction symbols on those segments to indicate they are parallel.)

∠B ≅ ∠FCE

C. Alternate interior angles theorem — The referenced angles are on opposite sides segment BC, which is your first clue. Your second clue is that the other legs of these angles (AB and CF) are given as parallel. These are alternate interior angles between the parallel lines AB and CF where transversal BC crosses them.

∠BED ≅ ∠CEF

D. Vertical angles are congruent — You will recognize these are vertical angles where segment DF crosses segment BC.

ΔBED ≅ ΔCEF

B. Angle-Side-Angle (ASA) — The previous three steps showed that two corresponding angles and the side between them are congruent in the referenced triangles. Hence the triangles are congruent by ASA.

DE ≅ FE and DB ≅ FC

A. CPCTC — These are corresponding segments of the triangles that were just shown to be congruent.

AD ≅ DB and DB ≅ FC ⇒ AD ≅ FC

H. Transitive property of congruence — This property says that two things congruent to the same thing are congruent to each other. Like a lot of geometry theorems, it seems to state the obvious.

ADFC is a parallelogram

G. AD and FC are congruent and parallel — The point of previous steps is to show AD and FC are congruent. The fact that AB is parallel to FC is a given, so now we have all the necessary parts to conclude that these two segments are congruent and parallel.

DE ║ AC

E. Definition of a parallelogram — We showed two sides are congruent and parallel, so the figure is a parallelogram. That the figure is a parallelogram allows us to conclude the other two sides are congruent and parallel. This is like CPCTC, but for a parallelogram instead of a triangle.

answered: Guest

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answered: Guest

he kicked it up? is this the answer ?

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Me to match this proof this is very difficult for me
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