Basic trig question to proof FA = BG

Ok--I'm a little confused as to what is given and what is not. And what are you trying to prove? Could you throw a little light on this?
 
firemath said:
Ok--I'm a little confused as to what is given and what is not. And what are you trying to prove? Could you throw a little light on this?
Click to expand...


Nothing but those letters to proof the side FA = BG

The others indicate lines that are parallels
 
OK...that's fine.

Given those parallel lines, what parallelograms do you see?
 
In parallelogram \(MNAF\) we have \(\overline{MN}\cong\overline{AF}\)
In parallelogram \(MNGB\) we have \(\overline{MN}\cong\overline{GB}\)
Why is that the case? What does that tell you?
 
pka said:
In parallelogram \(MNAF\) we have \(\overline{MN}\cong\overline{AF}\)
In parallelogram \(MNGB\) we have \(\overline{MN}\cong\overline{GB}\)
Why is that the case? What does that tell you?
Click to expand...

That is what the solution says but to prove this in detail
 
Justrandom1 said:
That is what the solution says but to prove this in detail
Click to expand...
pka said:
Click to expand...
In parallelogram MNAFwe have ¯¯¯¯¯¯¯¯¯¯¯MN≅¯¯¯¯¯¯¯¯AF
In parallelogram MNGB we have ¯¯¯¯¯¯¯¯¯¯¯MN≅¯¯¯¯¯¯¯¯GB
Why is that the case? What does that tell you?
Click to expand...
Those are well known (Euclid) theorems - about triangle and parallelograms.

Are you expected to provide proof of those?
 
Justrandom1 said:
Yes proof of those two sides mentioned are equal
Click to expand...
Line segments congruent to each other are equal in length.
Equality and congruent are both transitive relations.
\(\overline{FA}\cong\overline{MN}\cong\overline{BG}\) implies \(AF=BG\).
That is the proof.
 
I just noticed that you called this a "basic trig question", whereas all of us are seeing it as a geometry question that you can prove by showing that certain parts are parallelograms (or by other similar means). You also indicated that you expected to see lengths and angles in such a problem, which makes more sense in the context of trig.

It doesn't strike me as something I would use trigonometry for, but you probably could, if that is what is asked for. You could just label some segments and angles with variables, and work out others in terms of those. When you want a number and there isn't one, give it a name (a variable)!

Please tell us the context of the problem, and state the entire problem in its original wording, so we can be sure what you are asked to do. What are you learning that this might be intended to give you practice with?
 
firemath said:
Ok--I'm a little confused as to what is given and what is not. And what are you trying to prove? Could you throw a little light on this?
Click to expand...
The OP stated the given, showed the diagram and stated what was to be proved. I guess you want to the see the proof as well. Come on!
 
You might like to try an approach using similar triangles:

Consider similar triangles EFG and EMN.
Using ratios of sides can you write (a + d)/a in terms of b and e?
What does d/a equal in terms of e and b?
(equation 1)

Using ratios of sides can you write (c + f + k)/c in terms of a and d?
(equation 2)

Now consider similar triangles MFB and EMN.
Using ratios of sides can you write (c + f )/c in terms of a and d?
(equation 3)

Can you use the third equation to simplify the second equation?
Are you able to determine the value of k/c ?
What do you conclude?E7627B80-B562-4A56-B6D7-B9FF004544B6.jpeg
 
Subhotosh Khan said:
https://www.freemathhelp.com/forum/goto/post?id=483443
Those are well known (Euclid) theorems - about triangle and parallelograms.

Are you expected to provide proof of those?
Click to expand...
I thought that the definition of a parallelogram is a quadrilateral where both pairs of opposite sides are parallel and congruent. Then the proof follows just as pka stated.

@Subhotosh Khan: Why would you say that these are well known theorems as opposed to definitions? Can you please tell me your definition of a parallelogram? I know that some people use a different definition and prove a theorem which I would call the definition. Just curious. Thanks!
 
Jomo said:
The OP stated the given, showed the diagram and stated what was to be proved. I guess you want to the see the proof as well. Come on!
Click to expand...
My goodness...I never knew anyone so argumentative.

What if I was confused? Eesh...
 
Jomo said:
I thought that the definition of a parallelogram is a quadrilateral where both pairs of opposite sides are parallel and congruent. Then the proof follows just as pka stated.

@Subhotosh Khan: Why would you say that these are well known theorems as opposed to definitions? Can you please tell me your definition of a parallelogram? I know that some people use a different definition and prove a theorem which I would call the definition. Just curious. Thanks!
Click to expand...
"I thought that the definition of a parallelogram is a quadrilateral where both pairs of opposite sides are parallel and congruent." - NO!

The definition of parallelogram is: A quadrilateral with parallel sides

The congruence of the sides come as a corollary of the parallel sides.

That property of the parallelogram needs to be used here. Although Euclid's original work does not define parallelogram (explicitly) - that definition (quadrilateral with parallel sides) was included later.


(I threw in the triangle for good measure!!)
 
Subhotosh Khan said:
"I thought that the definition of a parallelogram is a quadrilateral where both pairs of opposite sides are parallel and congruent." - NO!
Click to expand...
Actually yes that is exactly the most commonly used definition for parallelogram: SEE HERE or HERE .
The operative words are pairs of parallel sides.
 
You must log in or register to reply here.
Top