In the figure above, Which of the following must be true?
Select an Answer
Choice C is correct. Given that is similar to , students can determine that the corresponding angle BAC is congruent to angle CED. The converse of the alternate interior angle theorem tells us that . (Students can also use the fact that and are congruent to make a similar argument.)
Choice A is not the correct answer. This answer may result from multiple misconceptions. The student may have visually identified the segments as perpendicular and used the wrong notation to express this statement.
Choice B is not the correct answer. This answer may result from visual inspection of the diagram. The line segments appear to be perpendicular, but need not be, given the information provided.
Choice D is not the correct answer. This answer may result from misunderstanding either the notation or the vocabulary of parallel and perpendicular lines. The student has incorrectly identified or notated parallel lines as perpendicular.
Students must use spatial reasoning and geometric logic to deduce which relationship is possible based on the given information. Students must also use mathematical notation to express the relationship between the line segments.