SOLUTION: Hello.
I have the following question:
In the figure W=X=Y=45 degrees. XB is perpendicular to WY, YA is perpendicular to WX. If WZ=10 find XY.
I know that the answer is 10 but
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Triangles
-> SOLUTION: Hello.
I have the following question:
In the figure W=X=Y=45 degrees. XB is perpendicular to WY, YA is perpendicular to WX. If WZ=10 find XY.
I know that the answer is 10 but
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Question 388975: Hello.
I have the following question:
In the figure W=X=Y=45 degrees. XB is perpendicular to WY, YA is perpendicular to WX. If WZ=10 find XY.
I know that the answer is 10 but I am not sure why. Can anyone help?
Thanks. Found 2 solutions by richard1234, robertb:Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website! Draw the angle bisector of X onto WB, and label that point Q. Then triangle WXB is symmetrical to triangle WAY, and XQ = 10. Angle QXB = 22.5 since XQ is an angle bisector.
It can easily be shown that triangle XZY is isosceles. Since angle XZY = 135, then angle ZXY = 22.5. Thus, XB is an angle bisector of angle QXY, and then it can be shown that triangles QXB and YXB are congruent. Finally, since QX = 10, it follows that YX = 10.
You can put this solution on YOUR website! Let BY = x. Then BZ = x also, because angle BZY would also be 45 degrees.
Since WZ = 10, and BZ = x, then by the Pythagorean Theorem, WB = . Incidentally, since triangle WBX is a 45-45-90 triangle, BX = also. Now apply the Pythagorean Theorem on the right triangle XBY: . Hence, , or XY = 10.
