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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.

 Feb 28, 2019
 #1
avatar+98130 
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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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