Question

In the figure below, ∠DEC ≅ DCE, ∠B ≅ ∠F, and segment DF is congruent to segment DB. Point C is the point of intersection between segment AG and segment BD, while point E is the point of intersection between segment AG and segment DF.

The figure shows a polygon comprised of three triangles, ABC, DEC, and GFE.

Prove ΔABC ≅ ΔGFE.

Answer 1

http://learn.flvs.net/webdav/assessment_images/educator_geometry/v15/module05/05_08_3b.jpg

Answer 2

can't go there

Answer 3

maybe new linnk?

Answer 4

@Vispla22

Answer 5

we can first prove that CAB and GF are congruent angles because of vertical angles

Answer 6

they also gve us the information that abc is equal to efg

Answer 7

do you mean CAB is congruent to GFE?

Answer 8

CB should also be equalt to ef fo the angles to be the same

Answer 9

no acb and gef

Answer 10

sorry i mistyped

Answer 11

ok . so far we have acb and gef are congruent because they are vertical angles

Answer 12

yeah and dc is equal to de and cb is equal to ef

Answer 13

how would we justify that?

Answer 14

well, the angles have to be the same and the only way it would do that is if the lengths are equal

Answer 15

wouldn't work see?

Answer 16

ok so what do we have to do then?

Answer 17

oh wait... they give you the info that the two angles are the same so it would have to be an iscoceles triangle

Answer 18

that's why dc=de and cb=ef

Answer 19

getting the two angles of each triangle we can then prove that CAB is equal to EGF because of the triangle sum theorm