BG is perpendicular to EF; DG bisects angle EDF

Question

prove that triangle DEG is congruent to triangle DFG

Answer 1

Hello,Tarynn,

    You have given information and you have to prove that ΔDEG≅ΔDFG (Triangle DEG is congruent to Triangle DFG).  Draw a model or drawing of the described object.  Then set up a formal proof.   You can prove that two triangles are congruent to each other through the following properties:  SSS (Every corresponding side of one triangle=the corresponding side of the other.);  SAS (Side-Angle-Side); ASA  (Angle-Side-Angle); AAS  (Angle-Angle-Side); HL (Hypotenuse-Leg).

Given:  BG⊥ EF  (BG is intersecting EF at a 90 degrees.); DG bisects <EDF (DG cuts angle EDF into two equal parts.)

Prove:  ΔDEG ≅ΔDFG  (Prove Triangle DEG is congruent (equal to) Triangle DFG)

                

                  ↑         

               B .

                  l                                 

    E____ 90⊥90º __F

              G |      ⁄

                 |    ⁄

              D .  ⁄   

                 ↓

I tried to draw the model for you, but I could not make the system draw the last segment ED. Here is most of the proof.  I would like you to try to finish it:  If you have further problems, contact me again (Susan C. on WyzAnt).

_________________________________________________

Statements              |     Reasons   

1.  DG bisects ∠EDF      1.  Given

2.  BG⊥EF                    2.  Given

3.  ∠EGD=90º              3.  Definition of perpendicular

    ∠FGD=90º

4.  ∠EGD=∠FGD           4.  Substitution

5.  GD=GD                   5.  Reflexive Property

6.  ∠EDG≅∠GDF            6.  Definition of bisection

7  ΔDEG≅ΔDFG              7.__________________    What property above justifies that these two triangles are congruent?  Please finish the proof.    Then it is done!                    

                                                      Thank you,    Susan C.