# Thread: Help in proving these two line segments are congruent?

1. ## 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

2. ## Re: Help in proving these two line segments are congruent?

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

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.

3. ## Re: Help in proving these two line segments are congruent?

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?

4. ## Re: Help in proving these two line segments are congruent?

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.

5. ## Re: Help in proving these two line segments are congruent?

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?

6. ## Re: Help in proving these two line segments are congruent?

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

I need help proving BF is congruent to ED
where are points H and K on your diagram?

7. ## Re: Help in proving these two line segments are congruent?

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.

9. ## Re: Help in proving these two line segments are congruent?

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).

10. ## Re: Help in proving these two line segments are congruent?

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?

11. ## Re: Help in proving these two line segments are congruent?

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

12. ## Re: Help in proving these two line segments are congruent?

Originally Posted by skeeter
no
Huh?

13. ## Re: Help in proving these two line segments are congruent?

Originally Posted by Crayola
Huh?

Parallelogram - Wikipedia, the free encyclopedia

14. ## Re: Help in proving these two line segments are congruent?

Originally Posted by Also sprach Zarathustra
Oh because of the alternate interior angles....

15. ## Re: Help in proving these two line segments are congruent?

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

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