Q:

# The coordinates of the vertices of quadrilateral DEFG are D(β2, 5) , E(2, 4) , F(0, 0) , and G(β4, 1) .Which statement correctly describes whether quadrilateral DEFG is a rhombus? Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length. Quadrilateral DEFG is not a rhombus because there is only one pair of opposite sides that are parallel. Quadrilateral DEFG is not a rhombus because opposite sides are parallel but the four sides do not all have the same length. Quadrilateral DEFG is not a rhombus because there are no pairs of parallel sides.

Accepted Solution

A:
Quadrilateral DEFG with coordinates of vertices of D(-2,5), E(2,4) , F(0,0) , and G(-4,1) is indeed a rhombus because it has opposite sides that are parallel, and all four sides are of the same length. This also means that the quadrilateral has equal opposite obtuse angles and equal opposite acute angles.
The passage contains a geometric question about whether a quadrilateral with given coordinates is a rhombus, and it provides an answer to this question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Q:

# The coordinates of the vertices of quadrilateral DEFG are D(β2, 5) , E(2, 4) , F(0, 0) , and G(β4, 1) .Which statement correctly describes whether quadrilateral DEFG is a rhombus? Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length. Quadrilateral DEFG is not a rhombus because there is only one pair of opposite sides that are parallel. Quadrilateral DEFG is not a rhombus because opposite sides are parallel but the four sides do not all have the same length. Quadrilateral DEFG is not a rhombus because there are no pairs of parallel sides.

Accepted Solution

A:
Quadrilateral DEFG with coordinates of vertices of D(-2,5), E(2,4) , F(0,0) , and G(-4,1) is indeed a rhombus because it has opposite sides that are parallel, and all four sides are of the same length. This also means that the quadrilateral has equal opposite obtuse angles and equal opposite acute angles.
user
The passage contains a geometric question about whether a quadrilateral with given coordinates is a rhombus, and it provides an answer to this question.

TYPE: SINGLE_QUESTION_WITH_ANSWER