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)
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
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.