Help with Proofs

ninax3

New member
Joined
Jan 19, 2006
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9
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

Full Member
Joined
Oct 30, 2004
Messages
466
Your picture is too blurry.
 

ninax3

New member
Joined
Jan 19, 2006
Messages
9
yeah i know. i couldn't get it any clearer, but i'll try again.
Can you still see it though?
 

happy

Full Member
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Oct 30, 2004
Messages
466
See how nicely your letters look? Trace your diagram the same way.
 

ninax3

New member
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Jan 19, 2006
Messages
9
Ok, I got the picture.
I did my best on paint..the triangles are supposed to be congruent.
 

Mrspi

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Dec 17, 2005
Messages
2,128
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.....
 

ninax3

New member
Joined
Jan 19, 2006
Messages
9
Thank you!
 
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