SOLUTION: Consider triangle ABC and trapezoid DEFG in the following image and use them to answer the questions below. Triangle ABC is a right triangle and trapezoid DEFG is isosceles.
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Question 1041428: Consider triangle ABC and trapezoid DEFG in the following image and use them to answer the questions below. Triangle ABC is a right triangle and trapezoid DEFG is isosceles.
https://byuis.brainhoney.com/Resource/46824920,0/Assets/Media/Images/41.6-HOT1-Proofs.jpg
a. Describe how to find the lengths of segments W, X, Y and Z. Show your answers for this question. Explain how you can be confident your calculations are correct.
b. Describe how to find the angle measures of angle DEG, angle DGE, angle EDG and angle ABC. Explain how you can be confident your calculations are correct.
c. Are there any segments or angles you can’t calculate based solely on the information in the image? Why?
d. If we drew a median into trapezoid DEFG and the given measurement of that median was 21.425, would that change your answer for part c of this question?
Thanks in advance!!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Triangle ABC and triangle EGF are congruent by ASA, so corresponding parts are congruent. That means y is either 25 or 
depending on whether you believe the label on segment AB or the one on GF. Also, w is either 29.15 or 
also based on the placement of your faith in the labels. One thing for certain is that at least one of those labels is an approximation and not the true value.
z is 15 because the trapezoid is isosceles and since we can determine angle DEG by the equality of opposite interior angles formed by the transversal of parallel lines, we can use the Sine Rule to calculate an approximation of x:
}\ =\ \frac{x}{\sin(28^{\circ})})
John
My calculator said it, I believe it, that settles it
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