For the given diagram, it has been proved that angle A is congruent to angle B.
Given Information:
Angle A and Angle B are such that,
Ray AC ║ Ray BE
Ray AD ║ Ray BF
Proof:
Since a straight line is the shortest line connecting two points in a plane,
Extend ray AD and ray BE, such that both intersect at point G.
Now, since, angle A and angle 1 both make corresponding angles,
∠A = ∠1 .......... (1)
Ray ADG is parallel to the ray BF.
Thus, again, angle B and angle 1 make corresponding angles,
∠B = ∠1 ............ (2)
From (1) and (2), as per transitive relationship of angles,
∠A ≅ ∠B
Hence proved.
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