1. ## parallel lines

In the figure , JG bisects $\displaystyle \angle DGH$ , the line FG is parallel EK , and KJ is parallel to GH . Prove that EJ is parallel to FH

2. Originally Posted by thereddevils
In the figure , JG bisects $\displaystyle \angle DGH$ , the line FG is parallel EK , and KJ is parallel to GH . Prove that EJ is parallel to FH
DEK and DFG
DJK and DHG
not difficult to prove them similar to each other, right? there are some parallel lines....

Then, you can prove that DE : DF = DJ : DH (= DK : DG). together with common angle D, you can eventually prove the 3rd pair of similar triangles, DEJ and DFH. And since they are similar, angles DEJ = DFH, and finally...

3. Originally Posted by ukorov
DEK and DFG
DJK and DHG
not difficult to prove them similar to each other, right? there are some parallel lines....

Then, you can prove that DE : DF = DJ : DH (= DK : DG). together with common angle D, you can eventually prove the 3rd pair of similar triangles, DEJ and DFH. And since they are similar, angles DEJ = DFH, and finally...
Thanks Ukorov , i got it . But this is the continuatino of the question whihc i am unsure of :

Prove also that $\displaystyle \frac{DE}{EF}=\frac{DG}{GH}$

4. Originally Posted by thereddevils
Thanks Ukorov , i got it . But this is the continuatino of the question whihc i am unsure of :

Prove also that $\displaystyle \frac{DE}{EF}=\frac{DG}{GH}$
$\displaystyle \frac{DE}{EF} = \frac{DK}{KG} = \frac{DK}{KJ} = \frac{DG}{GH}$