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If we knew the angle measure of one more angle, we could determine whether quadrilateral GOAL was a trapezoid or not.

Which angle is it? What would its measure have to be in order for GOAL to be a trapezoid? Explain your reasoning and cite any postulates or theorems you use.

joshalex768 Feb 28, 2019

#1**+1 **

If angle OAL = 70° GO would be parallel to LA

To see this.....extend LA in the direction of A to E

Then angle OAL + angle OAE sum to 180°

But angle OAE = 180 - angle OAL = 180 - 70 = 110

Then angles GOA and OAE are equal

And if this is so....then transversal OA makes alternate interior angles GOA and OAE equal....so....

A transversal cutting lines (segments) so that alternate interior angles are equal means that the lines (segments) are parallel

So...GO is parallel to LA.....and a trapezoid must have one pair of sides parallel

CPhill Feb 28, 2019