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.

 Feb 28, 2019

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



cool cool cool

 Feb 28, 2019

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