# Help with Proofs

#### ninax3

##### New member
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!!

#### ninax3

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

#### happy

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

#### ninax3

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

#### Mrspi

##### Senior Member
ninax3 said:
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.....

Thank you!