Triangle A-C-D has a line B-E from A-C to A-D. A-B is 6, B-C is 3, A-E is 12 and E-D is 9.
A student examines the triangle shown above. He notices that lines
and
look parallel. The student claims that they are parallel by look alone.
Is the student correct?
A.
Yes, because
.
B.
Yes, because
.
C.
Yes, because
.
D.
No, because
.
B.
Yes, because the triangle A-C-D is a right triangle based on the given sides and angles, and the line B-E is an altitude drawn from vertex A. In a right triangle, the altitude drawn from the right angle is perpendicular to the hypotenuse. Therefore, line B-E is perpendicular to line A-D, which means lines A-D and B-C are parallel.