Karen is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below
No triangle. Cannot copy and paste here.
To prove that segment DE is not parallel to segment BC, Karen is using an indirect method, also known as a proof by contradiction. This method involves assuming the opposite of what we want to prove, and then showing that it leads to a contradiction or inconsistency.
To follow Karen's approach, we first assume that segment DE is parallel to segment BC.
Next, we need to find a contradiction or inconsistency that arises from this assumption. One possible approach is to look at the angles formed by the intersecting lines. If DE is parallel to BC, then corresponding angles should be equal.
Since segment DE intersects segment AB at point F, we can compare angles AFE and CFD. If DE is parallel to BC, then angle AFE should be equal to angle CFD.
To measure angles, we can use the established principles of geometry. If we have the measurements of other angles in triangle ABC, we can use them to find the values of angles AFE and CFD.
Once we have the values of angles AFE and CFD, we can compare them. If they are equal, it would support the assumption that DE is parallel to BC. However, if we find that they are not equal, it will lead to a contradiction.
If we find that angles AFE and CFD are not equal, we have successfully shown a contradiction to our assumption. Therefore, we can conclude that segment DE is not parallel to segment BC in triangle ABC.