great thinker problem

[truth83]

given 3 lines I can make several parallel lines to create similar triangles, etc. But I am stuck. I keep solving it in terms of another unknown.

 

[Deleted member 4993]

given 3 lines I can make several parallel lines to create similar triangles, etc. But I am stuck. I keep solving it in terms of another unknown.

What "other unknown" - show it!

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

[url]http://www.freemathhelp.com/forum/th...Before-Posting[/URL]

 

[stapel]

Great Thinker Problem #6:

In the figure of the triangle, Lines EG, EF, FH, and FG intersect as shown:

\_ a|                   _ /
  \_|E               _ /
    |\_           _ /
    |  \_     _ /
    |    \_H/     a: 63*
    |    _ /_               |EH| = |FH|
    | _ /    \_   b: 32*
-___|/F        \_
b_ /|---___      \_
/   |      ---___  \_
    |            ---_\_
    |                G \--

Without a protractor, determine the measure of angle FGH.

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given 3 lines I can make several parallel lines to create similar triangles, etc. But I am stuck. I keep solving it in terms of another unknown.

I'm sorry, but it is not possible for us to help you find errors in working that we cannot see.

For instance, you started by noting that the two sides FH and EH have the little "congruent" marks on them, telling you that they have the same length. What sort of triangle, then, is EFH? Given what you know about vertical angles, what can you say about the measure of angle HEF? Given what you know about (that sort of) triangles, what then can you say about the measure of angle HFE? Given what you know about vertical angles, what can you say about the measure of angle HFG? What then can you say about the measure of angle HFG? Given what you know about the angle sum of any triangle, what then can you conclude about the requested angle?

And so forth. Please be complete. Thank you! ;-)

 

[pka]

given 3 lines I can make several parallel lines to create similar triangles, etc. But I am stuck. I keep solving it in terms of another unknown.

Consider Angle EFG.

\(\displaystyle m\left( {\angle EFG} \right) = 95 \) WHY? From there it is simple.

 

[Deleted member 4993]

given 3 lines I can make several parallel lines to create similar triangles, etc. But I am stuck. I keep solving it in terms of another unknown.

No parallel line is needed for this proof - as far as I can see...