A student examines the triangle shown above. He notices that lines BE and CD look parallel. The student claims that they are parallel by look alone.
Is the student correct?
To determine if lines BE and CD are parallel, we need to examine the triangle and consider the angles formed by these lines. If the corresponding angles are equal, then the lines are parallel.
In the given triangle, angle A = angle C (both are right angles). Additionally, angle D = 90 degrees - angle B and angle E = 90 degrees - angle C = 90 degrees - angle A. So angle D = angle B.
Since angle D = angle B, we can conclude that lines BE and CD are indeed parallel based on the angles formed by these lines. Therefore, the student is correct in stating that they are parallel.