Help with Proofs

[ninax3]

Given: FN is the perpindicular bisector of OE; ON is congruent to EF.
To Prove: ON // EF

& the pic looks like this :

THANK YOU SO MUCH iF YOU HELP ME!!

 

[happy]

Your picture is too blurry.

 

[ninax3]

yeah i know. i couldn't get it any clearer, but i'll try again.
Can you still see it though?

 

[happy]

See how nicely your letters look? Trace your diagram the same way.

 

[ninax3]

Ok, I got the picture.
I did my best on paint..the triangles are supposed to be congruent.

 

[Mrspi]

Given: FN is the perpindicular bisector of OE; ON is congruent to EF.
To Prove: ON // EF

& the pic looks like this :

THANK YOU SO MUCH iF YOU HELP ME!!

Since FN is the perpendicular bisector of OE, we can use the definition of perpendicular bisector to make two conclusions:
G is the midpoint of OE, and
Angles FGE and NGO are right angles.

Since G is the midpoint of OE, EG is congruent to OG.

Triangles FGE and NGO are right triangles. The hypotenuses are GIVEN to be congruent, and legs GE and OE are congruent. So, the triangles are congruent by Hypotenuse-Leg.

Angles E and O are corresponding angles of congruent triangles, so they are congruent. These angles are also alternate interior angles formed by transversal EO intersecting lines FE and ON. If a pair of alternate interior angles is congruent, then the lines are parallel.

If you need a two-column proof, I think I've given you everything you'll need to put one together.....

 

[ninax3]

Thank you!