The figure shows triangle DEF and line segment BC, which is parallel to EF:
Triangle DEF has a point B on side DE and point C on side DF. The line BC is parallel to the line EF.
Part A: Is triangle DEF similar to triangle DBC? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle DBC corresponds to line segment EF? Explain your answer. (3 points)
Part C: Which angle on triangle DBC corresponds to angle F? Explain your answer. (2 points)
Part A:
Yes, triangle DEF is similar to triangle DBC. According to the given information, line segment BC is parallel to EF. By definition, if two lines are parallel, then any line segments formed by these lines and intercepted by a transversal are proportional. In other words, the lengths of the corresponding sides of the two triangles would be in proportion, which is one of the criteria for triangle similarity.
Part B:
In triangle DBC, line segment BC corresponds to line segment EF. This is because BC and EF are parallel lines, and in a similar triangle, corresponding sides are proportional.
Part C:
In triangle DBC, angle D corresponds to angle F. Corresponding angles in similar triangles are congruent, which means they have the same measure. Since triangle DEF is similar to triangle DBC, angle D in triangle DBC corresponds to angle F in triangle DEF.