Given that , which of the following inequalities is correct?
and are corresponding angles formed by a line intersecting two parallel lines. So, .
If two angles of a triangle are equal in measure to two angles of
another triangle, then the triangles are similar. From the given figure, and share , and . Therefore, and their side lengths are proportional.
Since and , then .
The sum of a triangle's angle measures is . Therefore, in ,
For any triangle, if a side is longer than another side, then the angle opposite to the longer side is greater in measure than the
angle opposite to the shorter side. In ,
Since and , then it follows that is greater than half of .