College Geometry Help!

jennybenny02

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Joined
Oct 3, 2005
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15
Construct triangle[XYZ] such that <X is congruent to a given angle (say <D) and <Y is congruent to another given angle (say <E). Then XY+YZ+XZ = FG (FG is a given segment length which all sides of the triangle add up to.)

We use a compass and straightedge to solve this because we cant measure the given angles. I know how to construct a given angle w/ just a compass, but not sure how to put the rest of the problem together to show my steps how to make the triangle.
One of my classmates found a website with a problem just like this showing the steps and all, but Im not sure what that site was.

PLEASE, I need HELP!
 
Construct a triangle UVW using the two angles. UVW is similar to XYZ by AAA.
Construct a line UV+VW+WU parallel to FG. Draw FU and GW extended till they meet at Q. Draw QV and QW to FG. The intersections will divide FG into XY, YZ and ZX.
 
Ok, Im confused,

I understand what you mean by constructing triangle UVW using the two angles and making it similar to XYZ by AAA.

Im confused what you mean by ''Construct a line UV+VW+WU parallel to FG.'' and ''drawing FU and GW extended till they meet at Q.''

FG is just my given segment that the sides of teh triangle add up to. I guess IM confused about what you are making FU and GW mean.
 
Sorry, I got bogged down with using different letters for the same thing. Call the new line HI
Code:
H...............I
U.....V
      V.....W
            W...U
And 
F...............G
X.....Y
      Y.....Z
            Z...X
where we don't know how long the parts are.
What I was trying to say was
Code:
Q
|\
| \\
|  \ \
|   \  \
|    \   \
H  V  W   I
|      \    \
|       \     \
|        \      \
F.................G
X    Y     Z      X
(with another line QV to FG at Y
The parts of FG are proporional to those of HI (similar triangles) so we now have the sides of XYZ
I hope this is clear now.
 
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