# Help in proving these two line segments are congruent?

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• Aug 9th 2011, 12:06 PM
Crayola
Help in proving these two line segments are congruent?
Hello,

I need help proving BF is congruent to ED.

Givens:
Angle FBC is congruent to Angle EDA
The parallel sides of the parallelogram are congruent

http://i55.tinypic.com/fvihj8.jpg
• Aug 9th 2011, 12:39 PM
skeeter
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Crayola
Hello,

I need help proving BF is congruent to ED.

Givens:
Angle FBC is congruent to Angle EDA
The parallel sides of the parallelogram are congruent

http://i55.tinypic.com/fvihj8.jpg

using the fact that ABCD is a parallelogram along with the ASA postulate, you should be able to show triangle FBC congruent to triangle EDA ... then segments BF and ED are congruent because they are corresponding sides.
• Aug 9th 2011, 01:52 PM
Crayola
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by skeeter
using the fact that ABCD is a parallelogram along with the ASA postulate, you should be able to show triangle FBC congruent to triangle EDA ... then segments BF and ED are congruent because they are corresponding sides.

Well wouldn't that be for if we are trying to solve for triangle ACD and ABC?
• Aug 9th 2011, 02:00 PM
skeeter
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Crayola
Well wouldn't that be for if we are trying to solve for triangle ACD and ABC?

same result ... make a choice and go w/ it.
• Aug 9th 2011, 02:14 PM
Crayola
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by skeeter
same result ... make a choice and go w/ it.

But how would proving triangle ACD and ABC prove that DH and KF are congruent?
• Aug 9th 2011, 02:18 PM
skeeter
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Crayola
But how would proving triangle ACD and ABC prove that DH and KF are congruent?

Quote:

I need help proving BF is congruent to ED
where are points H and K on your diagram?
• Aug 9th 2011, 02:25 PM
Crayola
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by skeeter

where are points H and K on your diagram?

Sorry I got confused. Yes it should've been BF and ED.
• Aug 9th 2011, 02:29 PM
skeeter
Re: Help in proving these two line segments are congruent?
• Aug 9th 2011, 02:46 PM
Also sprach Zarathustra
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Crayola
Hello,

I need help proving BF is congruent to ED.

Givens:
Angle FBC is congruent to Angle EDA
The parallel sides of the parallelogram are congruent

http://i55.tinypic.com/fvihj8.jpg

Angle FBC is congruent to angle EDA - given.

BC=AD - The parallel sides of the parallelogram are congruent

Angle BCA is congruent to angle CAD - WHY?

From the above we can conclude that:

triangle FBC congruent to triangle EDA. (ASA)

So, BF=ED (corresponding sides on congruent to triangles).
• Aug 9th 2011, 03:00 PM
Crayola
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Also sprach Zarathustra
Angle FBC is congruent to angle EDA - given.

BC=AD - The parallel sides of the parallelogram are congruent

Angle BCA is congruent to angle CAD - WHY?

From the above we can conclude that:

triangle FBC congruent to triangle EDA. (ASA)

So, BF=ED (corresponding sides on congruent to triangles).

Alright, thank you! And for isn't Angle BCA is congruent to angle CAD because of the definition of an angle bisector?
• Aug 9th 2011, 03:01 PM
skeeter
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Crayola
Alright, thank you! And for isn't Angle BCA is congruent to angle CAD because of the definition of an angle bisector?

no
• Aug 9th 2011, 03:03 PM
Crayola
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by skeeter
no

Huh?
• Aug 9th 2011, 03:09 PM
Also sprach Zarathustra
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Crayola
Huh?

Parallelogram - Wikipedia, the free encyclopedia
• Aug 9th 2011, 03:12 PM
Crayola
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Also sprach Zarathustra

Oh because of the alternate interior angles....
• Aug 9th 2011, 03:15 PM
Also sprach Zarathustra
Re: Help in proving these two line segments are congruent?
Quote:

Originally Posted by Crayola
Oh because of the alternate interior angles....

Indeed!
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