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.
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