M:C:MC:12

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Additional Topics in Math

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The figure presents line segments A E and B D that intersect at point C. There is a horizontal line above point C that passes through points A and B, where A is to the left of B, and there is a horizontal line below point C that passes through points D and E, where D is to the left of E. A note under the figure says that the figure is not drawn to scale.

In the figure above, $increment A B C space tilde space increment E D C.$ Which of the following must be true?

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$stack A E with bar on top parallel to stack B D with bar on top$

Correct Answer:

$stack A E with bar on top perpendicular stack B D with bar on top$

Correct Answer:

$stack A B with bar on top parallel to stack D E with bar on top$

Correct Answer:

Yes

$stack A B with bar on top perpendicular stack D E with bar on top$

Correct Answer:

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Choice C is correct. Given that $triangle A B C$ is similar to $increment E D C$ , students can determine that the corresponding angle BAC is congruent to angle CED. The converse of the alternate interior angle theorem tells us that $stack A B with bar on top parallel to stack D E with bar on top$ . (Students can also use the fact that $angle A B C$ and $angle C D E$ 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.

Question Difficulty:

medium

Objective:

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.

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Question 16 of 30

M:C:MC:12

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