Geometry Question (1 Viewer)

[HeroWise]

Well. this is the question: In a quadrilateral ABCD, a line AF parallel to BC meets BD in F and a line BE parallel to AD meets AC in E. Prove that EF is parallel to CD

 

[pikachu975]

Not sure if I'm misunderstanding the wording but... if A is top left, B is top right, C is bottom right, D is bottom left, then AF being parallel to BC (right side of rectangle) means AF must be on the line AD (left side of rectangle) but either extended above or below it. But AF meets BD (diagonal going from bottom left to top right) meaning F is the same point as D? I don't get it but I think EF and CD are the same line lol maybe I misinterpreted it...

 

[HeroWise]

Ill provide a diagram which i think is right. This question is from a Text book (idk the name of it). But this diagram is mine:

 

[pikachu975]

Ill provide a diagram which i think is right. This question is from a Text book (idk the name of it). But this diagram is mine:

lol oops thought it said rectangle

 

[HeroWise]

I think I need to froof triangle OFE and ODC

I know Angle DOC is common I need to prove one more side for AA similarity proof

 

[Brian Tien]

to me i'd try to prove angle OEF is equal to angle OCD, because there you can say that the two lines are parallel because corresponding angles are equal and only equal when the lines are parallel. I can't think of a way to do that though right off the top of my head right now.

 

[HeroWise]

THats the problem

 

[HeroWise]

Problem solved! I used 3 Similar traingles and proved that the two triangles are similar to prove that they are parallel. SAS was the proof I used!